In his first speech since being elected head of Hamas' political bureau, the group's leader Ismail Haniya hailed what he described as a "new page" in relations between Hamas and Egypt.
Speaking to supporters in Gaza on Wednesday, Haniya reaffirmed the group's policy of not interfering in Egypt's internal affairs, saying Hamas will not allow the Strip to be used as a shelter or haven for anyone who intends to harm Egyptian national security.
The group also stressed in a statement on Wednesday its respect and appreciation for Egypt's historical role in supporting the Palestinian cause.
The statement pointed to the last week's talks between Hamas and Egyptian officials in Cairo, which it says "have led to some results that will help ease the situation in Gaza."
The statement added that the talks also touched upon the resumption of Palestinian national reconciliation efforts.
Relations between Egypt and the Palestinian Islamist group, which rules the Gaza Strip, were strained in the wake of the ouster of Egypt's Islamist president Mohamed Morsi in July 2013.
Cairo had accused Hamas of backing Egypt's banned Muslim Brotherhood organisation and smuggling arms through tunnels under the Gaza-Sinai border.
Egypt had also accused members of Hamas of involvement in the 2015 assassination of Egyptian prosecutor-general Hisham Barakat.
Since the start of this year, top Hamas officials have payed several visits to Cairo for talks with Egyptian officials.
In early 2017, Hamas leader Mahmoud Al-Zahar said that the group's relations with Cairo were witnessing improvement, evidenced by the reaching of an agreement on border control between Gaza and Egypt.
In an unprecedented move in February, Hamas, which was founded in 1989, rebranded itself in its new manifesto as an Islamic national liberation movement, rather than a branch of the pan-Arab Muslim Brotherhood, which has been outlawed in Egypt.
Last month, a delegation headed by Hamas' newly elected political bureau leader in Gaza Yahya Sinwar visited Cairo and discussed the humanitarian situation in the besieged Gaza Strip and Egypt's role in alleviating the siege.
In late June, Egypt trucked 1 million litres of cheap diesel fuel to Gaza's sole power plant to temporarily eased a crippling electricity crisis in the Strip.