The Spanish archdiocese announced on Thursday in response to an enquiry from katholisch.de that it condemns any kind of aversion towards the Holy Father.
The two priests had been informed that they would have to publicly ask forgiveness for their words because they had offended the ecclesial community and outraged the faithful.
"The Archdiocese of Toledo in no way accepts responsibility for the statements made."
Furthermore, the archdiocese does not rule out the possibility of reprimands against the priests in the future.
Several Spanish and Latin American priests - including two from the Archdiocese of Toledo - had said in a live video on YouTube that they would pray for the death of Pope Francis.
"I pray a lot for the Pope, that he goes to heaven as soon as possible," said one of the clergymen from Toledo.
Most of the others echoed this intention and said they would also pray for Francis' speedy death.
"Then let us pray even more fervently," added the other priest from Toledo afterwards.
The clerics recorded the video on 22 February, the feast of the Cathedra Petri - the Holy See.
On a traditionalist YouTube channel, the priests discussed hand communion, which they are fundamentally opposed to, at a "counter-revolutionary priests' regulars' table", as they themselves described their online conversation.
The priests have since announced via the platform "X" (formerly Twitter) that they were misunderstood. They had spoken about the Pope "in a humorous way".
The priests apologised for their careless choice of words.
One of the diocesan priests from Toledo is said to be one of the initiators of the petition against the Vatican's blessing document "Fiducia supplicans", reported the magazine "Vida Nueva" on Wednesday.
With the campaign, several priests from the archdiocese wanted to persuade Pope Francis to revoke the declaration of the Dicastery for the Doctrine of the Faith, which had allowed the blessing of homosexual and remarried couples under certain conditions.
In the Spanish church, Toledo is considered a hotbed of conservative clerics.