Police served warrants at a number of addresses beginning at 3 a.m. (0200GMT) local time, the force said. About 500 officers were involved in the operation, and searches were continuing at several locations, police said.
Greater Manchester Police said three people were arrested under the Terrorism Act, while five were arrested under immigration laws. Two others were released within hours.
Police would not comment on a report by Press Association, the British news agency, that said the arrests were related to terrorism in Iraq, the AP reports.
Todd said police and security agencies had been gathering intelligence "for at least a year, looking at the funding and support of terrorist activities overseas."
The Home Office indicated that at least five were not British citizens, and were detained under powers to deport people whose presence "is not conducive to the public good for reasons of national security."
One suspect was arrested in Liverpool in a joint operation by police and immigration officers, Merseyside Police said.
The other forces involved were London's Metropolitan Police, Birmingham's West Midlands Police and Cleveland Police in northeast England.