From left, Sen. Richard J. Durbin (D-Ill.), Sen. Harry M. Reid (D-Nev.) and Sen. Charles E. Schumer (D-N.Y.), the top three Democrats in the Senate. (Jonathan Ernst/Reuters)

So much for a neat, orderly succession for Senate Democrats.

Sens. Charles E. Schumer (N.Y.) and Richard J. Durbin (Ill.) remained at odds Wednesday over the future of their party’s Senate leadership, with aides to both men sticking by conflicting stories about a private conversation the veteran lawmakers had last week.

Durbin’s office insists that Schumer, who has the inside track to succeed retiring Sen. Harry M. Reid (Nev.) as the Democratic leader, vowed to support Durbin staying on as whip, the No. 2 leadership position. Schumer’s office said he made no such assurance.

The surprisingly contentious feud between the two former housemates has raised the question of whether Senate Democrats can resolve their hierarchy issues neatly or whether they will have to endure a messy intraparty fight moving toward the 2016 elections.

The Senate minority leader announced that he will not run for reelection in 2016. PostTV took a look back at Sen. Harry Reid’s (D-Nev.) time serving in the Senate. (Pamela Kirkland/The Washington Post)

The dispute exploded into public view Tuesday, and each side reaffirmed its position Wednesday, even as the senators opened lines of communication. Spokesmen for Durbin and Schumer said the senators spoke on the phone, but they declined to say what the senators discussed.

The spat comes just days after Reid triggered a leadership shuffle when he said that he plans to retire at the end of this Congress.

The dust appeared to settle quickly in the wake of Reid’s retirement announcement Friday. Reid swiftly backed Schumer, the third-ranking Democrat, to succeed him as leader in an interview with The Washington Post. Later, Durbin, the second-ranking Democrat, also voiced support for Schumer to become leader in an interview with The Post.

But a conversation that took place hours earlier — on the sidelines of the Senate’s all-night budget “vote-a-rama” — has become the source of intense dispute.

According to Durbin’s office, Durbin and Schumer came to an agreement during that chat in anticipation of Reid’s announcement.

“Senator Durbin took Senator Schumer aside and told him Senator Reid had asked to speak with him, and that Durbin thought it was to say he wasn’t running in 2016,” Ben Marter, a spokesman for Durbin, said in an e-mail. “Durbin told Schumer ‘you’ve earned this,’ that he wasn’t going to run for Leader, that he’d support Schumer, and that he intended to run for his own post again. The two senators agreed to support each other and shook hands on it.”

But Schumer spokesman Matt House denied that his boss had agreed to back Durbin.

“That’s not what happened but, regardless, Senator Schumer considers Senator Durbin a close personal friend,” House said in an e-mail.

For many years, Schumer and Durbin, both former House members, were Washington roommates. When Congress was in session, they shared a Capitol Hill rowhouse owned by then-Rep. George Miller (D-Calif.).

Miller, who retired from the House at the end of the last Congress, decided to sell the property, forcing Durbin and Schumer to find new living quarters.

The relationship between Schumer and Durbin has been strained in recent years by their rivalry in the top tier of party leadership and amid uncertainty about what would happen when Reid stepped down.

This week’s back and forth between Durbin and Schumer has played out with the Senate in a two-week recess, sparing them from awkward appearances alongside each other at leadership news conferences.

Durbin is the only Democratic senator who has said he plans to run for whip, but a wild card is Sen. Patty Murray (Wash.), currently the fourth-ranking Senate Democrat. Murray has not ruled out a run.

If Schumer were to publicly declare support for Durbin to continue as whip, he might risk alienating himself from Democratic senators who would rather see Murray ascend.

The offices for Murray and Durbin said that the two spoke Tuesday morning but did not say whether the whip position came up in the conversation.

“Senator Murray is focused on her current job and isn’t going to be speculating about other positions under Senator Schumer in leadership elections two years from now,” Eli Zupnick, a spokesman for Murray, said in an e-mail.

Marter said that Reid told Durbin on Friday morning that he would support him for whip. Reid’s office did not respond to a request for confirmation of that exchange.

Leadership elections for the next Congress will be held after the November 2016 elections.