Mazuronis did not tell reporters after the meeting if Grybauskaitė herself had asked him about his conviction, but he said that he had explained to the president that it had been a political case.
"We did not speak much about me, as the leader of the political party, having been convicted for signing the party's press release, as required by the statute. We only touched upon this. The president listened to what I said," he said after the meeting, which lasted about half an hour.
The candidate said that he had informed the president about his priorities for the Environment Ministry.
"No doubt, my first priority is to get (residential buildings) renovation off the ground by changing the system," he said.
Mazuronis said that his other priorities included waste management and easing conditions for construction in non-restricted areas.
"I got the impression that the president basically agrees that these problems need to be addressed," he said.
The politician said that he did not know if Grybauskaitė would approve his candidacy for the ministerial post.
He added that the president had not tested his English language skills during the meeting.
In a public statement issued in December 2003, Mazuronis, who was then the leader of the Liberal Democratic Party (now Order and Justice), accused Artūras Paulauskas of having sent Valery Ivanov, former leader of the anti-democratic movement Yedinstvo, to a rally of President Rolandas Paksas' supporters in Vilnius.
The statement came at the height of an impeachment scandal surrounding President Paksas.
Paksas was impeached in April 2004 and removed from office for gross violations of the Constitution.
A court has found Mazuronis guilty of slandering Paulauskas, who is now member of the Labour Party.