"I can say that the preliminary date of the first session of the lower house of parliament will be Monday, November 13, which is the fastest possible date taking into account constitutional norms," Duda said in a televised statement.
It came after the president this week met with the leaders of the country’s main political parties to discuss the formation of a new government.
Duda did not say whom he would task with forming a new government.
"Today we have two serious candidates for the position of prime minister, two political groups that claim to have a majority and have their own candidate for prime minister," Duda said.
"This is a new situation ... there has never been a situation where one party won and the others claim that they will have the majority," he added.
Poland’s ruling conservative Law and Justice (PiS) party has named outgoing Prime Minister Mateusz Morawiecki as its candidate to lead the new government after the October 15 parliamentary elections.
Meanwhile, three opposition groups that together command a majority in the new parliament have put forward opposition leader Donald Tusk, a former top EU official, as their prime ministerial candidate.
Tusk led Poland’s government from 2007 to 2014.
Opposition lawmakers said on Thursday that Duda's decision not to immediately name Tusk as a candidate for prime minister was unjustified given that other parties have ruled out working with the ruling conservatives, the Reuters news agency reported.
The ruling conservatives won Poland's October 15 election, but lost their parliamentary majority, increasing the likelihood of an opposition government.
The Law and Justice party, allied with two smaller groupings in a United Right coalition, claimed 35.4 percent of the vote and 194 seats in elections to the lower house of parliament.
Meanwhile, the largest opposition bloc, the Civic Coalition, led by Tusk's Civic Platform (PO) party, won 30.7 percent of the vote and 157 seats.
The centre-right opposition Third Way alliance finished third at the ballot box with 14.4 percent of the vote and 65 seats, and the opposition New Left party finished fourth with 8.6 percent and 26 seats.
The far-right Confederation group, with 7.2 percent of the vote, also crossed the 5-percent voter support threshold that Polish parties need to clear to enter parliament. It secured 18 lower-house seats.
The Civic Coalition, the Third Way and the New Left together hold 248 seats in the 460-seat lower house and have declared their intention to form a coalition government.
In addition to seizing control of the lower house, the opposition won 66 senatorial seats, while the ruling conservatives secured 34 seats in the upper house of Poland's bicameral parliament.
Under the Polish constitution, the new parliament must convene for the first time within 30 days of the election.
The president then has 14 days to nominate a candidate for prime minister. Once named, the nominee has 14 days to secure a vote of confidence from lawmakers. If this attempt is unsuccessful, parliament then selects its own nominee for prime minister.
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Source: IAR, PAP, Reuters