The two suspects were arrested on Newton Street in the Northern Quarter area of Manchester at 14:45 BST.
Detectives have obtained warrants of further detention for both men, meaning they can remain in police custody until 27 September.
Police confirmed searches at properties on Epworth Street in Liverpool and Lancaster Road in Salford had now been completed.
Evans, who is the senior national co-ordinator for CTP, said: “We are acutely aware this news will cause further concern to the Jewish community, as well as the wider public, especially given the significant High Holy day period.
“I want to reassure them we are working incredibly closely with colleagues in Greater Manchester Police and partners to ensure we’re doing everything we can to keep them and the wider public safe.
“And more broadly across the country, CTP is working with local police forces to provide protective security support and advice for areas with Jewish communities, and particularly during the High Holy Day period.”