WASHINGTON (Reuters) - U.S. Senate Majority Leader Mitch McConnell on Tuesday joined a chorus of Republican stalwarts publicly urging Marco Rubio to run for a second Senate term in Florida, as the party faces an uphill fight to maintain its control of the Senate.

Former Republican presidential candidate Senator Marco Rubio passes by reporter's after voting on Capitol Hill in Washington March 17, 2016. REUTERS/Gary Cameron

“We’re doing everything to encourage him to run,” McConnell said during an interview on MSNBC’s “Morning Joe” program.

Some political strategists and Senate Republican aides see a potentially weak field of Republican candidates for the Florida Senate seat and think Rubio could help Republicans hold their Senate majority if he entered the race.

He has until June 24 to decide if he wants to run in the Aug. 30 Republican primary.

Josh Holmes, a former McConnell chief of staff, said in a telephone interview that unlike many of the current Republican candidates for the seat, Rubio “still enjoys pretty high favorability and very high name ID ratings in Florida and the ability to raise a lot of money.”

Republicans now hold 54 of the chamber’s 100 seats. There are 44 Democrats and two independents who align themselves with the Democrats.

McConnell is trying to hold onto his job as Senate majority leader but with 24 Republican seats up for grabs in the Nov. 8 elections and only 10 Democratic seats in play, it will be a difficult bid.

Last week, Senate Foreign Relations Committee Chairman Bob Corker said in a statement that he had “strongly encouraged” Rubio to enter the race.

Rubio, a freshman senator elected in 2010, decided to retire from the Senate and instead seek the U.S. presidency.

But his effort came to an end in March after he was soundly defeated in the Florida Republican primary by Donald Trump, now the presumptive Republican nominee for the Nov. 8 election.

In a CNN “State of the Union” interview that aired on Sunday, Rubio was asked he if would ever seek public office in the future. “I think that’s a safe assumption,” he said, without elaborating.

During the interview, Rubio also said he would like to become commissioner of the National Football League.