On Monday, Sports Minister Joanna Mucha called on Grzegorz Lato to step down after Poland were knocked out after finishing bottom of Group A, failing to win any of their three Group A matches despite playing in front of enthusiastic home crowds.
"I don't see any reason for me to resign because the team did not advance out of the group," Lato told a news conference. "I and the association did everything for our team to prepare them for the Euros."
Lato, Poland's leading scorer at the 1974 World Cup, had vowed to "take a manly decision" and resign from his post at the Polish FA (PZPN) if Poland did not qualify for the quarter-finals.
Lato has fended off charges he has mismanaged the Polish FA and denied unproven accusations of corruption.
The domestic ruling soccer body has been under fire from politicians in recent years. Before Lato took over, a court appointed two temporary commissioners to run the organisation, but Poland backed down after protests from FIFA and UEFA.
Lato said he had already begun to look for a replacement for Franciszek Smuda as Poland's coach.
"After the loss with Czech Republic (in Poland's final group game), we started receiving proposals from Europe and even Brazil to take over as coach after Smuda," Lato said.
"We have a board meeting on June 27 and this question will be discussed there. It's not like I will think up a coach and serve him up on a platter."