WASHINGTON (Reuters) - Israel and Hamas militants should be able to close the remaining gaps in their positions in order to reach a ceasefire-for-hostages deal in Gaza, the White House said on Tuesday.

"We believe that these gaps can be closed," John Kirby, the White House national security spokesperson, told reporters as negotiators began gathering in Cairo for a fresh round of discussions.

Kirby said the Palestinian militant group Hamas had offered amendments on Monday to an original Israeli proposal aimed at ending the impasse.

The deal text, as amended, suggests the remaining gaps can "absolutely be closed," he said.

Israeli forces' seizure of the main border crossing between Egypt and southern Gaza raised fears that Israel might be beginning a much-feared incursion into Rafah.

Kirby said the Israelis had assured U.S. officials that the operation was of limited scope and duration and not a large-scale invasion.

(Reporting by Steve Holland and Doina Chiacu; Editing by Cynthia Osterman)