A tweet by the Rojava Committee of Sweden on Wednesday compared Erdogan to Italy's Fascist dictator Benito Mussolini, who was hung upside down after his execution in the closing days of World War II.

"History shows how dictators end up," the group wrote above a video showing pictures of Mussolini's 1945 execution and then a dummy painted to look like Erdogan swinging on a rope.

"It is time for Erdogan to resign. Take this chance and quit so that you don't end up hanging upside down on (Istanbul's) Taksim Square."

The Rojava Committee tweet came as NATO member Turkey piles pressure on Sweden and Finland to clamp down on Kurdish groups it views as "terrorists".

The Nordic neighbours still need Turkey to approve their NATO membership bids, which came in response to Russia's invasion of Ukraine.

Sweden, with its larger Kurdish diaspora, has particularly angered Turkey.

Ankara has dug in its heels during protracted negotiations that hinge on the extent to which Sweden is ready to meet Turkey's demand to extradite Kurdish suspects and prosecute groups such as the Rojava Committee.

It lashed out furiously Thursday at both the Rojava Committee and what it deemed as Stockholm's soft response to the tweet.

- 'Open debate' -

Erdogan's chief spokesman said Turkey condemned the Kurdish group's tweet "in the strongest possible terms.

"We urge the Swedish authorities to take necessary steps against terrorist groups without further delay," spokesman Fahrettin Altun tweeted.

His message came in direct response to a tweeted statement from Sweden's Foreign Minister Tobias Billstrom condemning the video.

Stockholm supports "an open debate about politics" but "distances itself from threats and hatred against political representatives", Billstrom wrote.

"Portraying a popularly elected president as being executed outside city hall is abhorrent," the Swedish diplomat wrote.

Billstrom's response did little to appease Ankara.

The Turkish foreign ministry summoned the Swedish ambassador for a dressing down, accusing Stockholm of going back on its past pledges and demanding that "the perpetrators of this action are found".

The angry exchange over a tweet came less than a month after Billstrom paid a cordial visit to Ankara in an effort to get the NATO membership bid over the line.

The Swedish government has since signalled that it has reached the limit of what it can do to meet Ankara's demands, particularly concerning the extradition of suspects.

Turkey has been battling a decades-long insurgency against the outlawed Kurdistan Workers' Party (PKK), which has claimed tens of thousands of lives.

But it has also used its fight against the PKK to justify prosecuting Kurdish politicians and support groups.

Turkey's top court is now weighing whether to ban the country's main Kurdish-backed party ahead of elections expected before June.