Statistics from Egyptian border crossing officials show a slight rise in the number of travelers back and forth, but there was no rush on the border from Gaza; no more than 900 Palestinians crossed during the fighting in any given day.
During a visit to Gaza, Brotherhood members played up their support for the territory and insisted they remained opposed to Israel.
"We came and saw innocent children being injured and killed by the Zionist war machine made in America," said Saad El-Katatni, a top leader of Morsi's party.
Egypt is at the heart of the mediation effort between Hamas and Israel over a truce. Israeli officials have converged on Egypt and met with security officials under Morsi, who had long refused to even use the name of Israel in public.
In a sign of the fine line the Brotherhood is treading, Amr Darag, a senior party member in charge of foreign relations, told the Foreign Policy Blog that if the offensive continued, the Egyptian government may consider opening the Rafah crossing permanently, "to facilitate support coming from any destination to Gaza."
Other officials fear such an open border would leave Egypt responsible for any future attack on Israel.
Highlighting the pressure on Morsi, ultraconservative leaders in Egypt's Sinai desert, which borders Gaza, have been pushing for him to take a more aggressive stance toward Israel. Morsi's party relies on electoral alliances with some of those leaders, who also play a role in keeping a lid on militancy inside Sinai.
"We don't care for the peace treaty (with Israel)," Sheik Marei Arar, a Salafi leader in Sinai, told The Associated Press. "We are seeking to unify the ranks of Muslims."
Hossam Sweilam, a retired army general, blamed the Brotherhood for the deteriorating security in Sinai, adding that the Egyptian military has been "paralyzed" in its efforts to chase extremists because of the Islamist alliance.
Associated Press writer Maggie Michael in Cairo contributed to this report.
Follow Sarah El Deeb on Twitter on https://twitter.com/seldeeb
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.