Interior Minister Habib al-Adly had said on Saturday after the bombings that killed 88 people that investigators were looking into possible links with those responsible for the 7 October attacks in the resorts of Taba and Nuweiba.
"The security services are looking for easy answers, but my clients are innocent," defence lawyer Sayed Fathi told AFP.
Mohammed Gaiez al-Sabah and Mohammed Rubaa Addallah appeared at the high state security court in Ismailiya, northeast of Cairo, but the third man, Mohammed Ahmed Salah Felifel is still at large and being tried in absentia.
When the trial opened on 2 July, the two men denied any involvement in the October triple bombings and said confessions had been extracted under torture.
A doctor was to examine the suspects to establish whether they had been tortured, but Fathi said that the report was not finished and that the trial had been adjourned until mid-August.
The three suspects are charged with premeditated murder, failure to surrender themselves, determination to kill Israeli tourists, terrorism and resisting the authorities during arrests.
According to human rights groups, up to 3000 people were detained when Egyptian forces swept the Sinai peninsula after the October bombings.