Republican members of the House Foreign Affairs Committee are expressing concerns about shadow diplomacy work by President Trump Donald John TrumpFederal prosecutor speaks out, says Barr 'has brought shame' on Justice Dept. Former Pence aide: White House staffers discussed Trump refusing to leave office Progressive group buys domain name of Trump's No. 1 Supreme Court pick MORE’s personal attorney Rudy Giuliani Rudy GiulianiThe Hill's Campaign Report: GOP set to ask SCOTUS to limit mail-in voting CIA found Putin 'probably directing' campaign against Biden: report Democrats fear Russia interference could spoil bid to retake Senate MORE in Ukraine.

Even as conservative Republicans are making public shows of their defense of the president, calling the impeachment inquiry unfair and storming the committee hearing room Wednesday, members of the committee tasked with oversight on foreign affairs are skeptical of the former New York City mayor’s involvement in overseas policy.

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Some say it's not completely abnormal for diplomacy to go through back channels, but they said it should not be the norm. And several said it generally shouldn't be done.

“I’m OK with that as long as they play within the confines of the law and don’t go beyond that,” Rep. Ted Yoho Theodore (Ted) Scott YohoKat Cammack wins Florida GOP primary in bid for Ted Yoho's seat The Hill's Convention Report: Democrats gear up for Day Two of convention Eyes turn to Ocasio-Cortez as she seeks to boost Biden MORE (R-Fla.) said. “Blanket OK — no. In certain areas, yes.”

Rep. John Curtis (R-Utah) called it “bad form” for outside officials to be tasked with foreign policy.

“My point is — this is not the first time this has been done,” he said. “Everything from former secretaries of State being involved with foreign policy to basketball players being involved with foreign policy, and I would say that I think all of those are in bad form.”

The criticisms show that even in the House, where GOP support for Trump in the impeachment inquiry is strong, some Republicans at a minimum are unnerved with actions by Giuliani and shadow efforts in general.

These criticisms are echoed in testimony in the impeachment inquiry, with witnesses saying former national security adviser John Bolton John BoltonJudge appears skeptical of Bolton's defense of publishing book without White House approval Maximum pressure is keeping US troops in Iraq and Syria Woodward book trails Bolton, Mary Trump in first-week sales MORE called Giuliani a “hand grenade” and described his involvement in a diplomatic side channel as a “drug deal.”

Secretary of State Mike Pompeo Michael (Mike) Richard PompeoWatchdog confirms State Dept. canceled award for journalist who criticized Trump Trump's push for win with Sudan amps up pressure on Congress Putin nominated for Nobel Peace Prize MORE on Sunday defended Giuliani’s role, however.

In an appearance on ABC’s “This Week,” he said it was “completely appropriate” and that “private citizens are often part of executing American foreign policy.”

Republican strategist Rick Wilson, a frequent critic of Trump’s on cable news, said House GOP members are caught in a dilemma. They risk incurring Trump’s wrath if they refuse to toe the president’s line, but they also don’t want to endorse activities they see as wrong — especially with polls showing growing support for the impeachment inquiry, especially among independents.

“If they [Republicans] were being honest with you, they would tell you they know this is a disaster, and they know this is a very bad call on the president and this team,” Wilson said.

Wilson said the climate has made it difficult for some Republicans to stay in Washington. He said he’d talked to one retiring House Republican who told him, “I would love to have stayed for years, but I can’t do it in this environment.”

To be sure, House Republicans this week were offering a firm defense of Trump while attacking the Democratic impeachment process.

Rep. Vicky Hartzler Vicky Jo HartzlerMissouri Rep. Vicky Hartzler wins GOP primary Wuhan is the final straw: The world needs to divest from China On The Money: Hopes fade for coronavirus relief deal this month | Burr problem grows for GOP | Layoffs hit record high of 11 million in March MORE (R-Mo.), a member of the House Armed Services Committee, said she stood up with other Republicans to protest the closed-door hearings of the impeachment inquiry, calling the process “unfair.”

House Minority Whip Steve Scalise Stephen (Steve) Joseph ScaliseGinsburg becomes the first woman to lie in state in the Capitol House GOP slated to unveil agenda ahead of election House panel details 'serious' concerns around Florida, Georgia, Texas, Wisconsin elections MORE (R-La.) called the process of the impeachment inquiry “a Soviet style process.”

Hartzler, however, stopped short of defending Giuliani and other officials, like U.S. Ambassador to the European Union Gordon Sondland and Energy Secretary Rick Perry Rick PerryEnergy secretary questions consensus that humans cause climate change OVERNIGHT ENERGY: Democrats push resolution to battle climate change, sluggish economy and racial injustice | Senators reach compromise on greenhouse gas amendment stalling energy bill | Trump courts Florida voters with offshore drilling moratorium OVERNIGHT ENERGY: Trump signs major conservation bill into law | Senate votes to confirm Energy's No. 2 official | Trump Jr. expresses opposition to Pebble Mine project MORE, who were involved with a Ukraine side policy.

“There needs to be coordination between all of government when we’re dealing with our allies who are talking about foreign policy,” said the congresswoman, who traveled on a congressional delegation to Ukraine this month.

Rep. Brian Fitzpatrick Brian K. FitzpatrickHopes for DC, Puerto Rico statehood rise Florida Democrat introduces bill to recognize Puerto Rico statehood referendum DCCC reserves new ad buys in competitive districts, adds new members to 'Red to Blue' program MORE (R-Pa.), one of two Republicans in districts won by Democratic nominee Hillary Clinton Hillary Diane Rodham ClintonBloomberg rolls out M ad buy to boost Biden in Florida Hillicon Valley: Productivity, fatigue, cybersecurity emerge as top concerns amid pandemic | Facebook critics launch alternative oversight board | Google to temporarily bar election ads after polls close Trump pledges to make Juneteenth a federal holiday, designate KKK a terrorist group in pitch to Black voters MORE in the 2016 presidential election who held his seat in the 2018 midterms, criticized Giuliani’s assignment to an outside diplomatic channel.

“That's a problem and it creates problems, as we're seeing now,” he told The Hill.

Those problems, he said, are of U.S. policy and strategy being undermined when outside officials flout established chains of command.

“Just like the military, the diplomatic chain, there's got to be integrity to the structure. There are rules and regulations governing to diplomatic communications. It's important that there be a consistent strategy amongst all the players. Anytime you have a situation where there's off-channel communications, that jeopardizes the whole system.”

Fitzpatrick, who was stationed in Ukraine for his work in anti-corruption with the FBI, said it’s important the U.S. speak with one voice and that Ukraine is reassured it enjoys bipartisan support on the Hill.

“My big concern right now — [Democratic Rep.] Marcy Kaptur Marcia (Marcy) Carolyn KapturUkraine language in GOP platform underscores Trump tensions Eye on gavel, Wasserman Schultz proposes panel on racial inequality in spending Overnight Defense: Army now willing to rename bases named after Confederates | Dems demand answers on 'unfathomable' nuke testing discussions | Pentagon confirms death of north African al Qaeda leader MORE and I have talked about this — we need to make sure that we still send a clear message that Ukraine still enjoys bipartisan support. Anytime you have a situation like this, that's always a concern. Ukraine is a very important ally to us.”