The Prime Minister, who heads the ruling centre-left Social Democrats-Green coalition, said his government would be meeting with opposition leaders to discuss the crisis, which has seen more than 86,000 people seek asylum in Sweden in 2015.
“I am ready to listen to all suggestions,” he said and added that any “party prestige” should not stand in the way of co-operation across the political blocs.
“Sweden faces enormous challenges and we should then also show the strength of a united Sweden.”
The debate comes just days after fresh figures by the country's Migration Agency revealed that more refugees have sought asylum in Sweden so far in 2015 than in any other year in the Nordic nation's history.
86,223 people have launched cases in 2015, surpassing a previous record set in 1992 when 84,016 people sought asylum in the Scandinavian country following fighting in the Balkans.
But the leader of the Moderates in the centre-right Alliance, Anna Kinberg Batra, launched a scathing attack on Löfven's government in Wednesday's debate, calling for tightened border controls and temporary residence permits.
“It is obvious that the situtation is not sustainable and that the government can't control it,” she said.
The heated debate also saw nationalist Sweden Democrat leader Jimmie Åkesson put forward a vote of no confidence in Finance Minister Magdalena Andersson for failing to plan for the refugee crisis, but this was immediately rubbished by leaders from both political blocs.
“You are about to turn this parliament into something far below its dignity,” said Löfven.
Åkesson announced the Sweden Democrats would put their support behind the Moderates' alternative budget proposal in a coming vote, Kinberg Batra replied her party would not support a vote of no confidence and ruled out seeking the nationalist's party backing.
“I am not prepared to rule with support by the Sweden Democrats,” she said.
Despite the controversy, Löfven's budget proposal is likely to pass in a vote later in October. The Alliance quartet indicated on Wednesday that plans to put forward four separate proposals – none of which would enjoy enough support on their own to overrule Löfven's bid – remained intact.
Concerns had previously been raised that the government's budget would fall after the Christian Democrat party pulled out of a cross-party deal to let it through parliament in a shock announcement on Friday.
But while party leader Ebba Busch Thor on Wednesday hinted that the four Alliance parties could put forward a common budget proposal as early as this spring, Kinberg Batra was quick to underline that no decision had yet been made.
The December Agreement was struck in late 2014 after Prime Minister Stefan Löfven's Social Democrat-Green coalition called a re-election because his budget fell in parliament. This happened because the nationalist Sweden Democrats backed the centre-right opposition's budget instead of abstaining from the vote as had been expected.