GAZA CITY — Hamas officials said Saturday that Egypt had informed them it would fully reopen the Rafah crossing on Sunday for the first time since the Aug. 5 border attack that killed 16 Egyptian soldiers, signaling a defrosting of relations that had been chilly since the killings.

Though Hamas, which rules the Gaza Strip, and the Muslim Brotherhood, which backs Egypt’s new president, Mohamed Morsi, share an ideology and political roots, the increasing closeness between the two governments had been interrupted by the attack.

Some in Egypt suggested that extremist groups in Gaza had supported the attackers, and Mr. Morsi not only shut down Rafah but also began destroying the hundreds of underground tunnels that supply the Gaza Strip with all manner of goods and Hamas with significant tax revenue.

On Saturday, Hamas also sent a delegation to Cairo to exchange information about the attack, according to a spokesman, who declined to provide further details. Egypt had previously sent Hamas a list of names of suspects, but Hamas had declined to make arrests, citing a lack of evidence.