"Until now, we have no idea about the disappearance of the Israeli soldier," Xinhua quoted the militant group as saying in a press statement.
"We do not know his whereabouts or the conditions of his disappearance," the group said.
Hamas added that a group of its fighters clashed at 7 a.m. Friday with advancing Israeli troops east of the southern Gaza Strip city of Rafah. However, it added that they have lost contact with this group who "apparently have been killed by Israeli fire."
"Our account is that the soldier might have been kidnapped and killed together with our fighters," the statement said.
On Friday, the Israeli government accused Hamas of breaching a 72-hour UN and US-mediated ceasefire after attacking Israeli forces deployed near Gaza, saying it has lost contact with one of its soldiers after Hamas militants carried out a commando attack earlier Friday against an Israeli military site near Rafah.
The security situation in Gaza has dramatically worsened hours after the humanitarian ceasefire came into force at 8 a.m. Friday as Israeli artillery fire killed more than 85 Palestinians in the southern Gaza Strip of Rafah.
More than 1,633 Palestinians have been killed and some 8,800 people injured since Israel stepped up an offensive on Gaza July 8.
Israel lost 61 soldiers and three civilians, including a Thai national.
Israel said its operation aims at ending Palestinian rocket fire into Israel, destroying "terror tunnels" sneaking into its territories.