Mr Mousavi, the leading presidential challenger, had called for the day of mourning and also demanded the release of a growing number of opposition politicians and journalists who have been arrested.
President Mahmoud Ahmadinejad was re-elected with almost two-thirds of the votes during the 12 June presidential election, but the opposition claims there was widespread fraud.
Guardian Council spokesman Abbasali Khadkhodai said a "careful examination" of the 646 complaints from the three candidates had begun.
"We decided to personally invite the esteemed candidates and those who have complaints regarding the election to take part in an extraordinary session of the Guardian Council on Saturday," he said.
A BBC correspondent at Thursday's Tehran rally
The crowd is enormous. It is impossible to put any kind of estimate on the numbers because it is so spread out. It starts down in a large square, Iman Khomeini square, and is filling the streets and avenues all around.
The most you can say is that there are several hundred thousand people here. And just like Mr Mousavi asked, the great majority are wearing sombre clothes. Many are in black, especially the women, who have turned out wearing black chadors.
It is, in effect, a funeral procession for the eight people who were killed here in Tehran on Monday, and the perhaps seven or so who have been killed in other parts of the country. But the most remarkable thing about this demonstration is the complete silence. The only sound is a certain amount of conversation. There is no shouting, no chanting - just a really dignified silence.
It is not known if the three candidates have accepted the invitation.
The BBC's Jon Leyne in Tehran says the candidates are unlikely to be wildly optimistic about the outcome. The Guardian Council - made up of six clerics and six lawyers - is traditionally loyal to Supreme Leader Ayatollah Ali Khamenei.
The council earlier this week said it would carry out a partial recount, but had ruled out a re-run of the poll demanded by Mr Mousavi.
However, opposition supporters are likely to be more encouraged by a statement from the Assembly of Experts - Iran's top clerical body responsible for appointing the supreme leader and, in theory, monitoring his performance.
"We congratulate the excited, epic-making and alert presence of 85% of the revolutionary people" in the election, the statement said.
It made no mention of the disputed result.
The Assembly of Experts is headed by former President Akbar Hashemi Rafsanjani, who is a strong supporter of Mr Mousavi and a key rival of Mahmoud Ahmadinejad.
The question now, our correspondent says, is whether Mr Rafsanjani will make his power play, and possibly challenge the supreme leader himself.
Hundreds of thousands of people were attending the latest protest rally in Tehran on Thursday after Mr Mousavi urged them to turn out in black in memory of those shot by members of the pro-government Basij volunteer militia on Monday.
There are about two or three thousand people here, all sitting in silence in the big courtyard inside the shrine. Police won't do anything because we are in a holy site
Ali, protester in Shiraz
Mr Mousavi, wearing a black shirt and suit, addressed the crowd with a loudspeaker, witnesses told news agencies.
The protesters had gathered in Imam Khomenei Square and marched north to central Tehran. Some held aloft pictures of those who died.
The BBC's Marcus George in Tehran says there was little sign of pro-government militia squads but supporters of Mr Mousavi have been telling each other to stick closely together for better protection.
Witnesses told AFP news agency the protesters were chanting "Peace be upon (the Prophet) Muhammad and his family" and were carrying placards with such slogans as "We have not had people killed to compromise and accept a doctored ballot box".
Reporter Marie Colvin of the UK's Sunday Times newspaper told the BBC from Tehran that both sides seemed to be trying to avoid major clashes but the situation was "a tinder-box, very edgy, so it's very hard to predict".
Former aide to Ayatollah Ruhollah Khomeini, leader of the 1979 revolution
Former deputy prime minister and the Islamic Republic's first foreign minister
Now leader of the banned but tolerated pro-democracy Freedom Movement of Iran
Iranians have continued to tell the BBC of their involvement in the protests.
One, Ali, was taking part in a silent sit-in at a shrine in Shiraz, south-western Iran, to remember those killed.
"There are about two or three thousand people here, all sitting in silence in the big courtyard inside the shrine. Police won't do anything because we are in a holy site."
In a counter-rally outside the prosecutor's office in Tehran on Thursday, hard-line students protested against the role of Mr Rafsanjani and his family.
Mr Rafsanjani's daughter, Faezeh, addressed supporters of Mr Mousavi on Tuesday.
The Fars news agency said on Thursday that Faezeh and her brother Mehdi had been barred from leaving Iran over their alleged role in the unrest.
Mr Mousavi and reformist former President Mohammad Khatami have sent a joint letter to the head of the judiciary asking for an end to "the violent actions against people and to free those arrested".
Iranian authorities have rounded up pro-reform figures and tried to further muzzle web sites and social networks used by opposition supporters to broadcast information and images of events in Tehran.
Ebrahim Yazdi, a foreign minister after the 1979 revolution and now leader of the Freedom Movement of Iran, was arrested while undergoing tests at a hospital in Tehran, a spokesman for his organisation said.
On Friday, Iranians will be listening closely to the address of Ayatollah Khamenei, who is due to deliver the sermon at Friday prayers.
Heavy restrictions have been placed on the BBC and other foreign news organisations. Reporters are not allowed to cover unauthorised gatherings or move around freely in Tehran - but there are no controls over what they can write or say.
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