Speaking from the Paris headquarters of his centre-right Republicans Party and surrounded by senior campaign chiefs, Fillon confirmed he had been summoned on March 15 in view of being placed under formal investigation - one step short of being charged.
Despite this, he said: "I won't give in. I won't withdraw, I will go all the way as beyond myself democracy is under attack.
"Yes I will be presidential candidate," he said.
Denying he had misused public funds, Fillon claimed that the investigation had been "biased against me from the start", and that it was unprecedented for judges to summon someone in view of placing them under formal investigation so soon after receiving the dossier of the case.
While he confirmed that he would attend the summons, he made it clear he would plough on whatever the outcome.
"Only universel suffrage and not a probe biased against me can decide who will be the next French president," he said.
Both Fillons deny any wrongdoing in a case dubbed "Penelopegate".
The affair has seen Fillon lose ground in opinion polls, with the latest suggesting he stands to be eliminated by Front National candidate Marine Le Pen and independent rival Emmanuel Macron in the first round of the presidential election on April 24.
Macron is polling to win in the runoff on May 8.
The magistrates handling the case have more powers than the financial prosecutor previously handling the case to investigate, including tapping phones or placing suspects under house arrest.
Fillon initially pledged to step down should he be formally placed under investigation. But he has subsequently promised to continue regardless, questioning the partiality of the investigation and saying it was for voters to decide whether he was fit to run the country.
The former Prime Minister enjoys parliamentary immunity as MP in Paris, and if he were to cite it, judges would have to issue a special request to have it stripped.
Under French law, the investigation would be suspended for the five-year presidential term should he be elected.
The Fillons have already been questioned by investigators but Penelope Fillon has declined to speak to the media.
At the weekend, her husband said: "Penelope is ready to talk, but for now I'm not for it. It's up to me to stand in the front line."
There had been media speculation that Fillon may step down and hand over to former Prime Minister Alain Juppé, who he beat in party primaries in November.