The first survey, published late on Wednesday, carried out by pollsters Pitagorica for TV channels TVI and CNN Portugal, gave the current premier Antonio Costa's PS party a 39.6% share of the vote, up from 37% last month.
Although it was one of the best recent results obtained by PS it leaves them just short of a majority, which under the proportional representation system, equates to between 42% and 45% of the vote.
The poll put the main opposition party, the Social Democrats (PSD), at 30%, down from 31.7% in December.
The second survey, by Intercampus for newspapers Jornal de Negocios and Correio da Manha, showed PS remained favourites to win but only grabbing 29% of the vote, edging down from 29.4% last month. It gave PSD 24.1%, up from 22.2%.
Intercampus said the number of undecided voters was around 18%.
In October, Costa's two former allies - the Communists and the Left Bloc - sided with right-wing parties to reject the minority government's budget bill, triggering the snap election.
If PS fails to win a full majority they will need the support of another party to pass legislation.
The Left Bloc and the Communists saw support at 6.4% and 5% respectively in the Pitagorica poll, and 7% and 4.9% in the Intercampus survey.
According to both polls, the Left Bloc remains the third largest party, closely followed by the rising far-right party Chega, polling between 4.9% and 5.7%.
Pitagorica surveyed 600 people on Dec. 30 to Jan. 9, with a margin of error of 4%. The Intercapus poll was carried out on Jan. 4-10 and surveyed 615 people. It had a margin of error of around 4%.
(Reporting by Sérgio Gonçalves and Catarina Demony; Editing by Nathan Allen, Alexandra Hudson)
By Sergio Goncalves and Catarina Demony
