Law Minister Salman Khurshid echoed party president Sonia Gandhi to counsel "patience" even as Rashtriya Lok Dal (RLD) leader and cabinet minister Ajit Singh said any Congress candidate would be fine.
Jammu and Kashmir's ruling National Conference, another Congress ally, vowed to back a Congress nominee.
Finance Minister Mukherjee himself was reticent, saying no decision had been taken on who the Congress hoped to field to succeed Pratibha Patil as India's 13th president.
Both Mukherjee and Ansari have emerged as front-runners, surprisingly getting support of even some in the BJP-led National Democratic Alliance.
Khurshid said the Congress was consulting its allies and other stakeholders.
On Friday, however, Odisha Chief Minister Naveen Patnaik, in Delhi to attend a conference, openly spoke against the Congress, becoming the first after the BJP to do so.
"It would be difficult to support a Congress candidate," the Biju Janata Dal (BJD) leader said.
Also Friday, Nationalist Congress Party (NCP) leader and former Lok Sabha speaker Purno Sangma said India had not had a tribal president in six decades.
He quickly added that this was the view of "the Adivasi community" and not of his party.
NCP chief Sharad Pawar said he would not react on the presidential race until the Congress picks a candidate.
Senior Congress leaders, including cabinet ministers, declined to speak on the issue, saying only the leadership would take the final call.
But there appeared to be palpable divisions on who the president should be -- Mukherjee, who some think is indispensable for the Congress, or Ansari, who too enjoys wide support.
Congress spokesperson Renuka Chowdhury had said Wednesday that Mukherjee was indispensable for the Congress, but she retracted after her comment caused confusion in political circles.
A section of the Congress feels a third name could crop up at the eleventh hour.
A presidential contest, if necessary, would be held in July.
After apparently taking allies NCP and DMK on board, the Congress is trying its best to rope in Trinamool Congress chief and West Bengal Chief Minister Mamata Banerjee.
After meeting Prime Minister Manmohan Singh Friday, she told reporters: "Our options are open. There has been no talk regarding candidature. There is time. If they (Congress) want to talk, they will let us know."
The Bharatiya Janata Party, whose initial opposition to Ansari and any Congress nominee was denounced by its ally Janata Dal-United (JD-U), said it was waiting for Congress to make a move.
"Some name came up yesterday, another today. Let the Congress formally announce its candidate, then we will comment," party leader Mukhtar Abbas Naqvi said.
The Left is open to both Mukherjee and Ansari, whose name it had suggested for the vice-president's post five years ago.
The Left parties will consult "other secular opposition parties before taking a final stand", said Communist Party of India leader A.B. Bardhan.
Samajwadi Party chief Mulayam Singh Yadav met Communist Party of India-Marxist general secretary Prakash Karat and Sitaram Yechury, who later met Pawar.
Hinting his party would support Mukherjee's candidature, Yadav Thursday said the president should be a political person. This is also the view of the DMK.
If the Congress and its allies secure the support of the Left and key regional parties, their nominee can win the presidential election. But the Congress prefers a pan-India consensus.