"I am resigning because there is too much pressure on the prime minister and the government," he told a press conference in Bangkok.
"I had no intention of insulting the monarchy. I will prove myself through the justice system."
He has been accused of insulting Thailand's king during a speech to the Bangkok foreign correspondents' club in August last year when he was part of a group opposed to the military-installed government then in power.
The offence of "Lese Majeste" is a serious charge in Thailand and can carry a lengthy jail term.
Police said late Thursday that they would formally charge Jakrapob and send his case to court for possible prosecution.
Jakrapob's speech last August was about the clash between democracy and what he called the "patronage system", but police have declined to specify what part of the speech allegedly insulted the king.
Protesters have been calling for the minister's scalp, as well the overthrow of Thailand's new government over its attempts to rewrite the country's constitution.
The People's Alliance for Democracy (PAD), a coalition of oppositon groups, has said it will hold a mass rally opposing the government on Friday evening.
The alliance was a key force in organising a series of street protests in the months before Thaksin Shinawatra, the then prime minister, was ousted in a bloodless coup in 2006.
"This government must take responsibility for its actions," said Suriyasai Katasila, a PAD spokesman.
"Our protests are extending beyond the charter amendments," he said.
But Selina Downes, Al Jazeera's correspondent in Thailand, said support for the opposition group appears to be dwindling and does not look like attracting the same sort of massive turnouts that preceded the 2006 coup.
|Thailand has seen at least 18 coups or coup |
attempts since 1932 [GALLO/GETTY]
On Thursday reports said Thailand's army has recalled one of its senior officers from a European trip, adding to speculation that the military was bolstering its ranks in preparation to stage a coup.
Thailand's military commander tried to dampen coup rumours on Thursday, but the ambiguity of his comments led some to believe that the military was planning to take action.
"No soldier wants to stage a coup to topple the government, but I cannot guarantee that there will be no more coup," General Boonsang Niempradit told reporters.
Giles Ungpakorn, a political science professor at Chulalongkorn University in Bangkok, told Al Jazeera the military would be making a big mistake if it were to launch another coup attempt.
"I think they would be mad to step in," he said.
"They need to consider the fact when they stepped in last time they did a terrible job. Nothing was resolved."
Political tension has been rising in Bangkok in recent days.
Earlier this week about two dozen people were wounded in clashes between anti-Thaksin protesters and his supporters at a rally in the capital.
Protesters accuse the government of Samak Sundaravej, the present prime minister, of trying to amend the constitution for political gain.
They say he is acting as a proxy for Thaksin and what they see as his efforts to maintain a behind-the-scenes hold on political power.
Thaksin spent more than a year in self-imposed exile following the bloodless coup but has since returned to fight corruption charges against him and his family.
Since the end of the absolute monarchy in 1932, Thailand has seen at least 18 coups or coup attempts.