"This tunnel was made by the hand of the fighters of (Izzadine) al-Qassam and they will not sleep in their efforts to hit the occupation and kidnap soldiers," the group's spokesman Abu Obeida told Hamas's al-Aqsa radio.
"We are working on the ground and under the ground to release the prisoners (held by Israel)," he said.
"Kidnapping soldiers is the only way to succeed against the (Israeli) occupation."
Israeli officials last Sunday said troops had uncovered a tunnel running from Gaza 450 metres (yards) into Israel and allegedly intended as a springboard for attacks.
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In June 2006 a group of Hamas and other militants snuck into Israel through a cross-border tunnel, seized Israeli soldier Gilad Shalit and took their prisoner back to Gaza the same way.
He was released on October 18, 2011 in exchange for 1,027 Palestinians held in Israeli prisons.
The trade was feted by Hamas as "an historic victory."
On Friday the Israeli army sent Palestinians in the Gaza Strip phone and text messages accusing the Islamist movement of putting its money into tunnelling projects rather than education and welfare for civilians.
"Know that Hamas is spending millions of dollars on tunnels used for hostile and terrorist acts against the state of Israel," the messages said. "This money should have gone to infrastructure, education and health projects."