"We have been cooperating 15 years and politically agree in all important issues and we will continue to do so," Pusic said when asked by the press about alleged disagreements between her and Cacic.
Pusic, who is the minister of foreign and European affairs, supported Cacic, saying his resignation would destabilise the government and Croatia, which she said was a factor of stability in Southeast Europe.
Regarding the party, she said the HNS talked about all problems.
Cacic was found guilty by the Kaposvar County Court on Friday of causing a car crash with two fatalities in Hungary in 2010 and was given a 22-month suspended sentence with three years' probation pending appeal.
Asked to comment on President Ivo Josipovic's statement that the government and the HNS should consider if Cacic could continue performing his duties, Pusic said this was her position too.
Pusic said she had no information that foreign diplomats were insisting on Cacic's resignation, adding that nobody mentioned this matter when she visited Brussels last week and that the ambassadors in Croatia had not mentioned it either.
Cacic too denied a possible split with Pusic, saying they were the founders of the HNS and that they always put general interest, and the interest of the party, before their own.
Cacic and Pusic were talking to the press in Sveti Martin, where the HNS was having a two-day meeting.