Morocco s Foreign Minister Nasser Bourita (C) arrives at the Conference Centre in the Algerian capital Algiers on October 29, 2022, ahead of the 31st Arab League summit next week. AFP
The invitation comes as Algeria hosts the first Arab League summit in three years, in the absence of several key figures including the Moroccan monarch.
Algeria cut ties with Morocco in August last year, alleging "hostile acts" following a string of diplomatic incidents and the collapse of a 30-year ceasefire in the disputed Western Sahara, a key point of tension between the neighbouring powers.
Tebboune had invited King Mohammed to the two-day summit which opened in Algiers on Tuesday, and the king had made public his intention to attend.
However, Foreign Minister Nasser Bourita told AFP that Algeria had sent "no confirmation via the appropriate channels" when Moroccan diplomats in Algiers asked how the monarch would be hosted.
Bourita's Algerian counterpart Ramtane Lamamra told a Saudi TV channel on Monday that the king's absence was a "lost opportunity".
Tebboune had said he would meet the king on his arrival in the Algerian capital, but Bourita said: "That kind of meeting can't be improvised in an airport waiting room.
"His majesty has given instructions to extend an open invitation to President Tebboune, because the dialogue was not able to take place in Algiers," Bourita said.
Mohammed VI has repeatedly called for reconciliation with Algeria and in a July speech voiced his desire for a return to "normal ties between brotherly peoples".
Morocco in late 2020 re-established ties with Israel and established security cooperation with the Jewish state, acts seen by Algeria as a threat to its interests.
That added to decades of mistrust fuelled by Western Sahara, a former Spanish colony seen by Morocco as an integral part of its territory, but where Algeria has long backed the pro-independence Polisario Front.