"I move without notice that the house ... agrees the resignation of the president of South Africa will take effect on September 25, " he said.
Mbeki stepped down, seven months before his second term as president was due to end, after the ANC asked him to, saying that party unity was at stake.
"I remain a member of the ANC and therefore respect its decisions," Mbeki said in a televised speech on Sunday.
"It is for this reason that I have taken the decision to resign as president of the republic following the decision of the National Executive Committee of the ANC."
MPs will vote on the appointment of Molanthe, who already has a position in the cabinet.
The ANC has dominated the parliament since the end of apartheid and the start of majority rule in May 1994.
Jacob Zuma, the ANC leader and the man expected to become president when elections are held in 2009, was not eligible to replace Mbeki at this stage because he is not a member of parliament.
|Tutu described Mbeki's resignation as the "settling of political scores" [AFP]
Mbeki had faced criticism over allegations that he pushed for corruption charges to be brought against Zuma.
A court ruling, handed down on September 12, threw out charges of corruption against Zuma, saying the prosecuting team violated some of his procedural rights.
Mbeki said the government "never compromised the right of the national prosecuting authority to decide whom it wished to prosecute or not to prosecute".
"This applies equally to the painful matter relating to the court proceedings against the president of the ANC, comrade Jacob Zuma," he said.
In an apparently concilatory move, Mathews Phosa, ANC treasurer-general, said on Sunday that the ANC wanted the current cabinet under the interim head of state.
"We want the cabinet to stay. We are very happy if they stay and we do these things together," he said.
The ANC has been divided since Mbeki sacked Zuma in 2005 as the deputy president, following corruption charges against him.
And the animosity has continued with Zuma's allies in the trade unions and the Communist party, as well as other critics, accusing Mbeki of being out of touch with millions of poor South Africans, despite his success in turning around the economy.
Archbishop Desmond Tutu, meanwhile, said that he was "deeply disturbed" by the resignation of Mbeki, which he described as the settling of political scores.
"I am deeply disturbed by recent events in our beloved country," he said.
"The so-called recalling of the president of our land fits the pattern of settling scores and the throwing about of weight that has happened post-Polokwane."
Tutu was referring to the ANC's Polokwane conference in December at which Mbeki was voted out of ANC leadership and replaced by his rival Jacob Zuma in a campaign that has divided the former liberation movement.
"Our country deserves better. The way of retribution leads to a banana republic," Tutu said.
"I am deeply disturbed that the nation ... has been subordinated to a political party."