Senate Republicans will host President Obama at their weekly conference lunch next week amid an intensifying effort by the White House to reach out to rank-and-file Republicans on a possible budget deal.

Senate GOP Leader Mitch McConnell Addison (Mitch) Mitchell McConnellGOP ramps up attacks on Democrats over talk of nixing filibuster MLB owner: It's 'very necessary' to vote for Trump Delta: Early departures saved flight attendants' jobs MORE (Ky.) announced the rare meeting between his conference and Obama in a press statement on Wednesday.

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“Senate Republicans welcome the president to the Capitol. And I appreciate he took my recommendation to hear from all of my members,” McConnell said in a statement.

Obama has also requested to meet with House Republicans next week, according to a notice sent to the conference Wednesday morning by Mike Sommers, chief of staff to Speaker John Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE (R-Ohio). The Speaker's office and the White House are now working on a time to schedule the meeting.

"President Obama has requested the opportunity to visit with our conference sometime next week to discuss various policy matters, and we are currently working to schedule that meeting. More details to follow," Sommers wrote.

The announcement that Obama will venture to Capitol Hill to meet the GOP conferences comes after the president spent the early days of this week courting a number of Republican senators in private phone calls — an indication that the president is looking to bypass party leadership in hopes of directly negotiating a long-term deficit-reduction bill.

In his statement, McConnell said Republicans welcomed the chance to discuss the nation's fiscal issues with Obama.

“We promised the American people that we would cut Washington spending, and the president signed those cuts into law. We have numerous challenges facing the country and Republicans have offered the president serious solutions to shrink Washington spending and grow the economy. And we will have an opportunity to discuss them with the president at the lunch,” he said.

Senate Republicans and Democrats meet to discuss policy at private caucus lunches each week. The lunches are used to hash out positions and discuss political strategy.

President Obama last met with Senate Republicans at a closed-door session in May 2010, in a discussion that touched on the BP oil spill and the possibility of strengthening security on the border. Response to that effort was mixed, with McConnell describing the exchange as "good" and "candid," but Sen. Pat Roberts Charles (Pat) Patrick RobertsThe Hill's Morning Report - Sponsored by National Industries for the Blind - Trump seeks to flip 'Rage' narrative; Dems block COVID-19 bill GOP senators say coronavirus deal dead until after election Trump says he'll sign USPS funding if Democrats make concessions MORE (R-Kansas) blasting Obama as too "thin-skinned."

Obama is also expected to visit the Democratic House and Senate caucuses, according to a report in The New York Times, which first reported the meetings.

The president has also invited nearly a dozen Republican senators out to dinner Wednesday night, the Times reported.

Obama's dinner invitations were extended to some of his most frequent antagonists in the Senate. According to CNN, those invited include Lindsey Graham Lindsey Olin GrahamGOP senators say coronavirus deal dead until after election Tucker Carlson accuses Lindsey Graham of convincing Trump to talk to Woodward Trump courts Florida voters with moratorium on offshore drilling MORE (S.C.), Bob Corker Robert (Bob) Phillips CorkerHas Congress captured Russia policy? Tennessee primary battle turns nasty for Republicans Cheney clashes with Trump MORE (Tenn.), Kelly Ayotte Kelly Ann AyotteBottom line Bottom line Bottom Line MORE (N.H.), John McCain John Sidney McCainCOVID response shows a way forward on private gun sale checks Trump pulls into must-win Arizona trailing in polls Nonprofit 9/11 Day bashes Trump for airing political ads on Sept. 11 anniversary MORE (Ariz.), Dan Coats Daniel (Dan) Ray CoatsThe Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump, Biden renew push for Latino support Former Intel chief had 'deep suspicions' that Putin 'had something on Trump': book Overnight Defense: Woodward book causes new firestorm | Book says Trump lashed out at generals, told Woodward about secret weapons system | US withdrawing thousands of troops from Iraq MORE (Ind.), Tom Coburn Thomas (Tom) Allen CoburnCOVID response shows a way forward on private gun sale checks Inspector general independence must be a bipartisan priority in 2020 Congress must protect federal watchdogs MORE (Okla.), Richard Burr Richard Mauze BurrRep. Mark Walker says he's been contacted about Liberty University vacancy Overnight Defense: Trump rejects major cut to military health care | Senate report says Trump campaign's Russia contacts posed 'grave' threat Senate report describes closer ties between 2016 Trump campaign, Russia MORE (N.C.), Mike Johanns Michael (Mike) Owen JohannsMeet the Democratic sleeper candidate gunning for Senate in Nebraska Farmers, tax incentives can ease the pain of a smaller farm bill Lobbying World MORE (Neb.), Pat Toomey (Pa.), Ron Johnson Ronald (Ron) Harold JohnsonRomney undecided on authorizing subpoenas for GOP Obama-era probes The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Trump, Biden couldn't be more different on climate change GOP chairman to release interim report on Biden probe 'in about a week' MORE (Wis.) and John Hoeven John Henry HoevenDavis: The Hall of Shame for GOP senators who remain silent on Donald Trump Bottom line Bipartisan senators seek funding for pork producers forced to euthanize livestock MORE (N.D.).

NBC News reported the dinner is scheduled for three hours Wednesday evening at the Jefferson Hotel in downtown Washington. The hotel hosted numerous fundraising events for the Obama campaign during the president's 2012 reelection effort.

A senior administration official said that Wednesday's meeting was part of Obama's latest "common-sense caucus," where the president wants to reach out to "moderates and pragmatists who are compelled to do the right thing."

"It's clear to get anything done there's going to need to be a coalition with moderates," the senior official said. "Clearly talking to Boehner John Andrew BoehnerLongtime House parliamentarian to step down Five things we learned from this year's primaries Bad blood between Pelosi, Meadows complicates coronavirus talks MORE has gotten us nowhere all the time. Now we're looking to reach out to people who want to work with us. He's trying to build on the idea of a common-sense caucus."

Asked why the president decided to meet with the senators for dinner on Wednesday night and speak to the group next week on the Hill, the aide added, "I think there's just a frustration that we were not getting anywhere with the leadership."

While the official said it's unclear whether reaching out to Senate Republicans will ultimately work, "It just takes a couple of votes. We have to get to 60 [votes] not 70. And if moderate Republicans joined Democrats in the Senate, it isolates the House."

"But we'll see ... we take them at their word that they want to work with us," the official said.

House Republicans welcomed the president’s entreaty with open – if skeptical – arms.

“Anytime he wants to talk to us is a good step,” said Rep. Lynn Jenkins (R-Kan.), the vice chairwoman of the House Republican conference.

The party has complained for years about Obama’s lack of engagement with Congress and more recently about the campaign-style rallies he continued to hold even after his reelection.

“He has been out on the campaign trail, and he has been trying to bully us instead of bargain with us, but it hasn’t worked. Maybe this is a recognition of that,” Rep. Tom Cole (R-Okla.) said. “Everybody is allowed multiple chances, and if we can find a more productive way to work back and forth together, particularly on these fiscal challenges, that’s all for the good.”

Conservative Rep. Phil Gingrey John (Phil) Phillip GingreyEx-Tea Party lawmakers turn heads on K Street 2017's top health care stories, from ObamaCare to opioids Beating the drum on healthcare MORE (R-Ga.) praised the new effort at dialogue, particularly since the president wanted to speak to the whole conference instead of merely one-on-one negotiations with Speaker John Boehner (R-Ohio), which rank-and-file members have bristled at.

“In my opinion, that can only be a good thing,” Gingrey said. “Now I don’t what he’s going to say or what he’s going to ask of us, but certainly I’ll be there, listening.”

At the same time, some Republicans were skeptical of the president’s motives. “I’m open-minded. I hope this is not check-the-box, so he can then tell [reporters], ‘Hey, look, I met with the Republicans,’ ” said Rep. Patrick Tiberi (R-Ohio), a senior member of the Ways and Means Committee and a Boehner ally. “So we’ll see.”

A House GOP leadership said the fact that Obama’s outreach was generating so much interest was, in itself, an indictment of the president’s leadership. “The president engaging with members of Congress should not be breaking news,” the aide said. “This is what presidents are supposed to do.”

The administration official said the idea was to move back to the start of the administration where there was outreach to the Hill.

On Tuesday, Obama spoke with Graham, who hinted that the president's efforts could be gaining momentum in the bitterly divided Congress.

“I’m very encouraged by what I see from the president in terms of substance and tone. He’s calling people — this is how you solve hard problems," Graham told reporters.

Obama also reportedly spoke with Sen. Susan Collins Susan Margaret CollinsGOP short of votes on Trump's controversial Fed pick Congress must save the Postal Service from collapse — our economy depends on it Garcetti: I would have acted sooner if Trump hadn't downplayed virus MORE (R-Maine), a key centrist vote, along with budget hawks like Corker and Coburn. Last week, Obama met with Graham and McCain at the White House, as well as separately with top House and Senate leadership from both parties.

—This story was first posted at 7:31 a.m. and last updated at 1:02 p.m.

Russell Berman and Amie Parnes contributed to this story.