Republican presidential candidate Ted Cruz said he did not support Donald Trump's controversial comments on Muslims Dec. 8. Cruz spoke as he announced proposed legislation on the resettlement of Syrian refugees. (Reuters)

Sen. Ted Cruz (R-Tex.) rejected Donald Trump's new proposal to restrict Muslims from traveling to the United States Tuesday, but refused to attack his rival, calling him a "friend."

"I disagree with that proposal. I like Donald Trump. A lot of our friends here have encouraged me to criticize and attack Donald Trump. I'm not interested in doing so," Cruz told reporters at a Capitol press conference, with Texas Gov. Greg Abbott (R) at his side to tout the senator's own legislative offerings.

Cruz, whose own campaign has steadily risen in recent weeks among conservative activists, distinguished his own plan to restrict refugees from regions ravaged by Islamic State forces from Trump's proposed blanket ban on all Muslim arrivals. However, the freshman senator continued to embrace the real estate titan's candidacy, which has focused on similarly sharp-edged proposals on immigration and other hot-button issues.

Cruz's reluctance to denounce Trump -- and praise for some of the moguls other proposals -- came in stark contrast to the response from other Republican presidential candidates and the party's senior leaders to the billionaire's controversial Monday proposal. Some candidates called it unconstitutional, and leaders of the Republican parties in Iowa and New Hampshire forcefully opposed the idea. House Speaker Paul D. Ryan (R-Wis.) told reporters that Trump's idea "not conservatism" and "not what this country stands for" after delivering the same message Tuesday morning to the GOP caucus.

[How Ted Cruz wooed and won Donald Trump]

Instead of joining the Trump critics, Cruz tried to tout his own proposals to restrict the flow of refugees: a three-year moratorium on any coming from nations where Islamic State forces are wreaking havoc, allowing governors to opt out of receiving any refugees and revoking citizenship for any American who travels abroad in support of Islamic State forces.

"Certainly in the media there has been no shortage of criticism for Donald Trump, and I do not believe the world needs my voice added to that chorus of critics," Cruz said Tuesday, highlighting his rival's tough immigration proposals to build a wall along the Mexican border. "And listen, I commend Donald Trump for standing up and focusing America's attention on the need to secure our borders. ... I think Donald Trump has done a good job of focusing  the American people's attention on the need to do so."

Cruz's campaign has been operating under a belief that his candidacy stands to benefit the most if Trump -- an unsteady campaigner whose statements grow more provocative with each month he remains atop the polls -- falters and falls out of contention. For months, Cruz has declined to attack other controversial Trump proposals he does not embrace.

[Read Paul Ryan's sharp criticism of Trump's new proposal to ban Muslim travel.]

Asked if he intended to support Trump if he were the GOP standard bearer next year, Cruz said yes, with some qualification: "I will absolutely support the Republican nominee, but I hope and intend for that nominee to be me."