Washington (CNN) Senior Senate Republicans are calling on Sen. Ted Cruz to rebuild his strained relationships with his colleagues and apologize to Majority Leader Mitch McConnell before the party establishment considers consolidating behind his presidential bid.

Cruz has increasingly called for Republicans to unify behind his candidacy in order to take down front-runner Donald Trump. But in interviews Tuesday with CNN, it's clear Cruz's fellow GOP senators are not willing to do that, at least not yet.

Republican senators said that Cruz must return to Capitol Hill and make the case directly to his colleagues to help ease long-festering tensions. And a large number of Republicans said the fence-mending starts with this: Apologizing to McConnell for calling him a liar last year on the floor of the Senate.

That message -- to smooth things over with Senate Republicans in a private session -- was personally delivered by fellow Texan and McConnell's chief deputy, Sen. John Cornyn, who spoke with Cruz by phone after the candidate won their home state's primary earlier this month.

"I actually made that suggestion to him when I talked to him last," Cornyn said when asked if he thought Cruz should apologize for his McConnell remarks. (A spokesman later said that Cornyn did not seek an apology but urged Cruz to speak directly to the Senate GOP Conference.)

Others had similar suggestions for Cruz.

"I think he's got some bridges to build here," said Sen. John Thune, the No. 3 Senate Republican. "I think it would be helpful obviously for him -- if he thinks he is going to be the guy or wants to be the guy -- to come back here to mend some of those fences that he tore down when he was here."

"That was not proper as you know, and I raised hell about it," Sen. Orrin Hatch of Utah, the longest-serving Senate Republican, said of Cruz's criticism of McConnell. "I'm a great believer of repentance and changing, and I think there's a gradual change there that I'm noticing, which is good."

Hatch also had this to say of Cruz: "It's always helpful when you admit you're wrong."

How far Cruz is willing to go to win back his colleagues remains to be seen.

Jeff Roe, Cruz's campaign manager, signaled that the Texas senator was unlikely to begin wooing his colleagues.

"It's not like we have some phone tree of U.S. senators to endorse," Roe said. "We never built our campaign that way."

Cruz calls for party to back him over Trump

Cruz is pushing for the party to unite behind him and has reached out to one of his former presidential adversaries, Sen. Lindsey Graham of South Carolina, who is among the few in the Senate GOP Conference prepared to back Cruz -- assuming Ohio Gov. John Kasich and Florida Sen. Marco Rubio drop out of the race.

Speaking Sunday in Concord, North Carolina, Cruz made the pitch for unity.

"I want to tell you that all across North Carolina and all across this country what we are seeing is Republicans coming together and uniting behind our campaign because ours is the only campaign that has beaten Donald Trump over and over again and can and will win this nomination," Cruz said.

The talk of renewing his relationship comes as the GOP establishment's last two favored candidates, Rubio and Kasich, face mounting questions about their viability. And although a number Republican senators are open to Trump as the nominee, some are patently fearful that the bombastic businessman will do lasting damage to the Republican Party.

'I'm not a member of any establishment or cartel'

Still, Cruz has only won the support of one of his colleagues, Utah Sen. Mike Lee, who announced his endorsement last week. And for other Senate Republicans, it hasn't been that easy to come to grips with the prospects of Cruz as the nominee.

Cruz has regularly attacked his colleagues on the campaign trail, calling them weak-willed and "mendacious" -- and essentially accusing them of corrupt backroom deal-making, saying they are part of the "Washington cartel." The rhetoric has made him a hero on the right as he's tapped into the anger with Washington, helping to elevate his presidential campaign as he tries to keep pace with Trump. But it has only served to infuriate his colleagues.

"I'm not a member of any establishment or cartel," scoffed Sen. Pat Roberts, R-Kansas, a Rubio supporter.

Since joining the Senate in January 2013, Cruz and his colleagues have repeatedly sparred bitterly over tactics and policy, most notably over the senator's demand to defund Obamacare, a battle that led to a 16-day government shutdown.

Cruz said he is fighting a GOP establishment unwilling to stand up for conservative principles. But many of his colleagues believe he picks unwinnable fights simply to promote himself.

"If he's asking someone for an endorsement from the United States Senate, I think he needs to go to that individual and explain what has changed since we were thrown under the bus," said Sen. Dan Coats, R-Indiana. "I think his conflict is: His narrative that has gotten him to where he has gotten is to throw us under the bus."

Asked if he thinks Cruz should apologize to McConnell, Coats said: "I think the decision he'll make will be based on his political strategy, not on maybe what's the right thing do."

Indeed, last year, things reached a fever pitch between Cruz and his colleagues when the Texas senator took to the Senate floor and accused McConnell of telling a "flat-out lie" over negotiations to move a major trade bill. McConnell, according to Cruz, privately said he did not woo wayward senators on the trade bill by promising to revive the controversial Export-Import Bank, the nation's chief export credit agency that is backed by business groups but reviled by some conservatives. McConnell later denied the charge.

When McConnell moved to the Export-Import Bank measure, Cruz erupted on the floor.

"I cannot believe he would tell a flat-out lie," Cruz said in a fiery floor speech.

On Tuesday, Sens. Jeff Flake, R-Arizona, and Mike Rounds, R-South Dakota, said it would be "helpful" for Cruz to apologize for those remarks if he wants the party to close ranks behind him.

"It's more difficult for him [to win support] because of remarks like that," said Flake, a Rubio supporter.