After four years, when his party won a two-thirds majority of seats by gaining 52% of the votes, Kövér appeared with short hair in the inaugural session of the sixth parliamentary term on 14 May 2010.

"[8] In September 2013, László Kövér said in a radio interview that in the long run he could image parliament should give more executive and legislative power to the cabinet in order to more effective treatment on "everyday challenges and enforce decisions through decrees, without the need to enact even the most detailed rules.

His words "we would like it if our daughters believed the highest level of self-actualization is to give us grandchildren" caused a media storm and spawned memes on the internet.

[12] In September 2019, during a summit devoted to Europe's demographic challenges, he suggested that childless people are "not normal" and stated that “having children is a public matter, not a private one”.

[13] In April 2021, he claimed in an interview that “the Hungarian leftwing liberal opposition is part of a globalist, anti-national network” and that its representatives are “no different from Mátyás Rákosi or Ernő Gerő”.

In November it was reported by the Hungarian investigative journalism outlet Direkt36 reported that Kövér had delivered a speech (which had been secretly recorded) when meeting Hungarian civil intelligence services at their private 30th anniversary event in February 2020, in which he claimed that the current opposition parties are "the greatest national security threat to the country", adding that “the other part of the political class is acting in the spirit of the political tradition of abandoning the state and of self-disparaging as a nation”, likening them to the Communists led by Béla Kun in 1919 and claiming that they are involved in a 'class war'.

The ceremony was attended by the leadership of the Jobbik party, and Hungary's State Secretary for Culture Géza Szőcs and speaker of the Hungarian Parliament László Kövér.

[15] Kövér, in his answer letter to Wiesel stated, the American, British and Soviet generals in the Allied Control Commission determined the conclusion in 1945 and 1947, when they refused to extradite the exiled writer two times for the request of the contemporary Hungarian Communist Minister of the Interior, Nyirő was not a war criminal, nor fascist or anti-Semitic.

[19] Kövér cited a Hungarian Jewish scientific review (the Libanon) and the newspaper stated that neither Nazi ideals nor anti-Semitism could be found in Nyírő's literary works.

[19] Nyírő, the Transylvanian-born Hungarian writer, deserves respect not because of his - although insignificant, but certainly tragically misguided - political activities but his literary works, according to Kövér.

"We are shocked by the reports that you chose to participate in an event commemorating anti-Semitic writer József Nyírő," wrote Rivlin, "By so doing, you have openly proclaimed your identification with a man whose party, as part of the Hungarian leadership, cooperated with the Nazi murderers in the execution of their plan to annihilate the Jewish people."

Rivlin also said: "A person who took part in such a ceremony cannot participate in an event honoring a man like Raoul Wallenberg, a Righteous Gentile, a symbol of humanity, who saved Jews while risking his life, and who serves as an example of the fight against the Nazis and their collaborators, with whom you chose to identify.

Kövér's words were strongly condemned by centre-left opposition and LGBT associations: Tímea Szabó (Dialogue for Hungary) described the statement as "shameful", while independent MP Bernadett Szél accused Fidesz to "court the far-right with no more inibitions".