The ruling Social Democrats and Greens, and their parliamentary ally the Left Party, are backed by 39.5 percent. The other bloc, centre-right Alliance coalition, that defined Swedish politics for a decade trails close behind on 38.5 percent.
The Swedish centre-left bloc holds a slim lead over the centre-right ahead of Sunday's national election, a survey showed, but both are short of a majority and the anti-immigration Sweden Democrats could yet emerge as the largest single party.
The ruling Social Democrats and Greens, and their parliament ally the Left Party, were backed by 39.5 percent, according to Friday's poll by Novus for public service broadcaster SVT.
The other of the two blocs that have defined Swedish politics for a decade, the four-party centre-right Alliance coalition, trailed close behind on 38.5 percent.
The nationalist Sweden Democrats scored 19.1 percent, well above the 12.9 percent they won in the previous election in 2014.
Those figures suggest political gridlock may be hard to avoid after Sunday's vote.
"I think we are facing an extremely complicated process to form a government, maybe the most complicated in modern times," said political scientist Niklas Bohlin at the Mid Sweden University.
TRT World's Simon McGregor-Wood reports from Stockholm.
Necessity of cooperation
Either some form of cooperation between the centre-left and Alliance or an accommodation with the Sweden Democrats is likely to be necessary.
But the two blocs have never governed in tandem, and so far all other parties have shunned the Sweden Democrats.
While most pollsters see the two blocs winning roughly equal support, the figures for the Sweden Democrats differ widely between surveys.
Ranging at about 16 to19 percent in the traditional polls based on phone calls, the nationalists score as high as 25 percent in some online surveys, which have often been seen as at greater risk of being skewed.
But the traditional polls greatly underestimated support for the Sweden Democrats before the previous election, while the online surveys were far closer to the result.
"It's not that they are shy voters, but that they are distrustful of the polling agencies," said Henrik Ekengren Oscarsson, a professor in political science at Gothenburg University.
"So the Sweden Democrats' sympathisers are not participating in these kinds of surveys."
Traditional pollsters have said they have altered their methods to better reflect the level of support for the Sweden Democrats.