Rassoul was seen as the favoured candidate of outgoing President Hamid Karzai, and his support for Abdullah could be decisive in deal-making to choose Afghanistan's next leader as US-led troops withdraw from the country.
Rassoul's own bid to become president gained little momentum and he came third with just 11.5 per cent in the first round of voting, but he remains an influential power-broker.
"I ask the people for the sake of national unity and political stability to vote for Doctor Abdullah, so that we win the election," Rassoul, who resigned as foreign minister to run in the election, told a press conference in Kabul.
The second-round vote will pit Abdullah against former World Bank economist Ashraf Ghani in a head-to-head battle, after the two came first and second in the eight-man election on April 5.
Neither candidate secured the 50 per cent needed for outright victory, with Abdullah gaining 44.9 per cent and Ghani on 31.5 per cent, according to preliminary results.
The official final first-round result will be announced on Wednesday after weeks of adjudication over fraud complaints.
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