GAZA CITY, Gaza Strip - Gaza's ruling Hamas movement has politicians sweeping streets to show community spirit, activists distributing chocolates and cards signed "from Hamas with love," and police visiting homes and schools to soften security forces' often harsh image.

The Islamic group - which Tuesday marks the anniversary of the movement's 1987 founding - says the outreach is simply a way to reconnect with Gazans after more than three years in control of the seaside territory. Hamas denies it has been losing ground, though one poll suggests that support for it has been slashed in half since its 2006 election victory.

The need to shore up popularity highlights the dilemma that has vexed Hamas since it seized Gaza from internationally backed Palestinian Authority President Mahmoud Abbas in 2007: In trying to be both a violent resistance movement and a responsible government, it often ends up satisfying neither its extremist core constituency nor people hoping for a better life.

Since taking power, Hamas has attempted a balancing act.

It has tried to cling to its extremist ideology, fearing that moderation would render it a politically irrelevant lesser copy of Abbas' pragmatic Fatah movement. But Hamas also largely halted attacks on Israel to avert punishing retaliation.

An informal truce, in place since Israel's war on Gaza two years ago, has not been enough to get Israel and Egypt to lift the border blockade they imposed after the 2007 takeover, although it has been eased in recent months. Gazans still overwhelmingly depend on handouts and struggle with more than 30 percent unemployment.

The level of support for Hamas is difficult to gauge, because Gazans are less inclined to speak freely for fear of repercussions. Hamas remains firmly in control, but some analysts say they detect growing impatience with Gaza's isolation, as well as with Hamas' efforts to enforce conservative Islamic mores and stifle dissent.

"Hamas' popularity has been declining while in power, mostly because of the living conditions under the blockade and mistakes ... such as human-rights violations and restrictions in freedom of speech," said West Bank-based pollster Walid Ladadweh, who measured a popularity drop in Gaza from 31.7 percent this summer to 23.9 percent in the fall. The poll of 1,200 people had a margin of error of 3 percentage points.

At the height of its popularity, after winning 2006 parliament elections in the West Bank and Gaza, Hamas had an approval rating of just over 50 percent, according to Ladadweh's Palestinian Center for Policy and Survey Research.

Hamas insists it is more popular than ever, and intends to prove it with a mass rally Tuesday. "After 23 years, Hamas became No. 1 in the hearts of the Arab and Palestinian people," said Fawzi Barhoum, a spokesman for the movement.

The turnout is closely watched every year, and Hamas has been working hard to ensure a large crowd.

During a Muslim holiday in November, about 12,000 Hamas activists went door to door, distributing boxes of chocolate to more than 300,000 families, said Ashraf Abu Daya, a Hamas official.

In the run-up to the rally, Hamas politicians helped clean Gaza's streets.

Last week, dozens of Hamas leaders and government officials swept and shoveled dirt and debris on Omar al-Mukhtar Street, Gaza City's main thoroughfare. In the Jebaliya refugee camp, Hamas lawmakers Mushir al-Masri and Ismail Ashqar walked the streets and took notes as residents talked about their problems.

The third campaign, to last for 50 days, is aimed at improving the image of the security forces, said Col. Kamal Abul Nada, who heads the effort.