European election observers say they have some concerns about the conduct of parliamentary and presidential elections in Romania.
Adrian Nastase's Social Democrats have already claimed victory
The OSCE observers said that although the election was well organised and professional, it may have been possible for some people to vote more than once.
With around half of the vote counted, the Social Democrats (PSD) have a small lead over the centrist opposition.
The presidential race looks set for a second round on 12 December.
The Social Democrats leader, and current prime minister, Adrian Nastase, is narrowly ahead of the centrist opposition Justice and Truth Alliance candidate, Traian Basescu.
While the Social Democrats announced their victory after exit polls on Sunday night, Mr Basescu believes he and his party still have a chance of winning.
He also called for an inquiry into voting irregularities.
The Organization for Security and Co-operation in Europe (OSCE) which has 18 international observers from 13 states at the elections, raised a number of issues.
"While the democratic election process appears to be further consolidated in Romania, some procedural concerns have been raised regarding suspension of the use of voter cards," said OSCE ambassador Stephen Nash.
"In the context of a closely contested election, this has the potential to affect public confidence,"
The independent Pro-Democracy Association, which had 3,300 monitors at polling stations, has also raised concerns about how allowing voters to use any polling station in the country could have opened the door to multiple voting.
Spokesman Adrian Sorescu said: "We are very concerned over the fact that the control of the number of votes made by each voter was almost impossible."
Observers say it was possible for people to make multiple votes
The governing Social Democrats have denied opposition allegations that they bussed supporters around the country to cast multiple ballots.
With around half of the vote counted the PSD had about 35% of the
vote, just three percent ahead of the centrist alliance.
In the presidential race, Mr Nastase led with nearly 39% of the vote over Mr Basescu's
But Mr Basescu was jubilant on Monday: "In real terms I think we have already won... because the estimated level of frauds is between three and five per cent."
The top two contenders are expected to face a second round of voting on 12 December to determine who has won the presidency.
The victor will replace Ion Iliescu, who is coming to the end of his second four-year term as president.
Around 18 million people were eligible to vote in Sunday's elections, in which 314 parliamentary and 137 senate seats were up for grabs.
The new authorities will have the task of steering the country towards a target date for EU membership in 2007.
The EU has criticised the current government for being too slow on structural reforms and corruption, while failing to secure human rights and free media.
The Social Democratic Party has enjoyed a stable period in government, with sustained growth and declining inflation.
It is credited with rescuing Romania from economic collapse, and has a slight lead in opinion polls.
The concerns about potential fraud in the elections have prompted comparisons with neighbouring Ukraine where rival presidential candidates have been involved in a stand-off since last Sunday's vote.