Sen. Marco RubioMarco Antonio RubioHouse immigration fight could boost vulnerable Republicans Venezuelan oil must not fall under Russia's tutelage Giuliani rails against Mueller probe MORE (R-Fla.) plans on briefing Republicans on progress in crafting an immigration reform bill during the next Republican policy luncheon.

Rubio, who has been involved in bipartisan negotiations on crafting an immigration reform bill, said he had been given the green light to update his Republican colleagues next week.

"Earlier this week, I requested and received permission to brief the entire Republican conference during our policy lunch next week. I look forward to briefing you at that meeting," Rubio wrote in a letter to four Senate Republicans on Friday.

Rubio's letter was in response to the four GOP senators, Mike LeeMichael (Mike) Shumway LeeGOP senators introduce Trump's plan to claw back billion in spending Trump has exposed Democratic hypocrisy on prison reform Denial of services to same-sex couples can harm their health MORE (Utah), Jeff SessionsJefferson (Jeff) Beauregard SessionsRick Santorum: Immigrant parents are putting children 'in peril' by coming to US border Emotion shouldn't serve as the basis for immigration law Giuliani insists Trump won't fire people to end Mueller probe MORE (Ala.), Chuck GrassleyCharles (Chuck) Ernest GrassleyDem senator: Trump Jr. may have given 'false testimony' about meeting with foreign nationals A second chance for Republicans to reform farm handouts Former US attorneys urge support for Trump nominee MORE (Iowa), and Ted CruzRafael (Ted) Edward CruzGOP senators introduce Trump's plan to claw back billion in spending Pro-Trump super PAC raises .5 million in 6 weeks Trump has exposed Democratic hypocrisy on prison reform MORE (Texas), who urged Rubio and other senators involved in the immigration negotiations to offer more transparency on the bill's progress.

The four senators sent a letter to the Republican senators in the so-called bipartisan Gang of Eight, urging them to release more details on their negotiations in crafting the immigration proposal. Members of the bipartisan group have recently said they plan to unveil their immigration reform bill soon.

"It is time for you to discuss the status of your negotiations, disclose what concessions have been made, and provide details to members of the Judiciary Committee as well as the entire Republican Caucus," the senators wrote in the letter, released Friday. "As members of the Judiciary Committee, we believe it is critical that the public and the entire Senate body be given adequate time to read and analyze the contents of any immigration bill put forth by the Majority. Our Committee has had only three hearings in recent months, barely touching on issues involving enforcement, border security or the creation of a temporary worker program."

They said that they were "deeply concerned" with recent statements made by Sen. Charles SchumerCharles (Chuck) Ellis Schumer'Right to try' is a win for patient rights and President Trump Overnight Finance: White House planning new tax cut proposal this summer | Schumer wants Congress to block reported ZTE deal | Tech scrambles to comply with new data rules OPEC and Russia may raise oil output under pressure from Trump MORE (D-N.Y.) that a basic agreement has been reached by the group on legalizing undocumented workers in the U.S. Schumer is one of eight senators involved in the talks.

"We should not further test the faith of the American people by implementing a major overhaul of the immigration system that prioritizes legalizing law breakers over the long-term needs of the country," their letter stated. 

"In that regard, we are deeply concerned by Senator Schumer’s recent statement that your group has “come to a basic agreement, which is that first, people will be legalized. In other words, not citizens, but they'll be allowed to work, come out of the shadows, travel. Then, we will make sure the border is secure," the GOP senators wrote.

  The senators wanted staffers to brief members of the Republican Committee staff by the end of Monday on the specifics of the immigration reform negotiations.

"Therefore, we ask that your staff be made available to brief Republican Committee staff no later than close of business on Monday, April 8," the senators wrote. "We also request that you personally discuss your group’s proposal with the entire caucus early next week so that all members can raise concerns and questions before the deal is finalized."

Senate Judiciary Committee Chairman Patrick LeahyPatrick Joseph LeahyMcConnell sets 'minibus' strategy for 2019 spending Dem senator mocks Pruitt over alleged security threats: 'Nobody even knows who you are' Pruitt tells senators: ‘I share your concerns about some of these decisions’ MORE (D-Vt.) recently told Rubio that he wanted to move quickly on moving the immigration bill to through his committee once it was unveiled.

"Because the President has failed to lead on this matter, your group has secretly met for months and not consulted with members of the Committee about major changes to our nation’s immigration laws," the senators wrote in the letter. "The time for transparency has come. Given the majority’s rushed timetable, we believe it is time for you to discuss the status of your negotiations, disclose what concessions have been made, and provide details to members of the Judiciary Committee as well as the entire Republican Caucus."  

--This report was updated at 5:10 p.m.