Estonia’s new interior minister has called the country’s first female president, Kersti Kaljulaid, an “emotionally heated woman” for walking out during the swearing-in of a cabinet minister accused of domestic violence.

Mart Helme made the sexist remark at a news conference where he also accused domestic news outlets of applying a double standard in covering abuse allegations against a former minister from his far-right party.

President Kersti Kaljulaid, the first woman to serve as the Baltic country’s head of state, left a Monday swearing-in ceremony for a new three-party government when it was time for the appointee at issue to take the oath of office.

Marti Kuusik was sworn in as technology and foreign trade minister along with the rest of prime minister Juri Ratas’s cabinet after news reports featured the domestic violence allegations.

Police opened an investigation to review the allegations hours later. Kuusik, a member of Helme’s Estonian Conservative People’s party (ERKE), resigned the next day but dismissed the investigation as being based on “slander” and “a terrifying media attack” against him.

Estonia’s interior minister, Mart Helme. Photograph: Ints Kalniņš/Reuters

In a statement he said: “Let me again confirm that the accusations made against me are slander – I am not someone who engages in violence.

“As of now, the decision of the prosecutor’s office to start criminal proceedings against me has been added to the terrifying media attack launched against me in recent days. In a situation like this it is not possible for me to carry out my work as minister. Furthermore, the rest of the government is not able to work normally.”

Helme called reporting on the allegations “an unconstitutional witch hunt”. He also made clear his dim view of the president’s decision to walk out during the ceremony and return to her seat when it was the next minister’s turn.

“An emotionally heated woman can afford to do that,” Helme told reporters. “But Kersti Kaljulaid is not simply a woman, but the president of the republic.

“She reads one article, becomes so emotionally upset as a woman that she makes a decision right away.”

Kaljulaid, who has been president since October 2016, did not respond on Thursday to Helme’s comments.

She attended the cabinet ceremony wearing a sweater printed with “Sona on vaba” which means “Speech is free”.

Helme and his son, newly appointed finance minister Martin Helme, have accused the news media before of displaying a negative bias toward their party.

The party has advocated abolishing legal recognition for same-sex civil unions, demanded changes to the abortion law and fiercely opposed European Union quotas for taking in asylum seekers.

Photographs of the two flashing the OK hand sign at Monday’s swearing-in ceremony have received attention from other politicians. The use of the familiar gesture by some extreme-right activists and white supremacists has given it an alternative meaning.

Mart Helme has not responded to questions about the gestures.

EKRE entered Estonia’s parliament in 2015. It emerged from elections on 3 March with 17.8% of the vote to become the third-largest party in the national legislature.

Associated Press contributed to this report