"Authority is not agitation," Juppé told a crowd of about 2,000 supporters in Chatou, near Paris.
"It's very easy to rush to extremes and that's what's happening today," he declared, criticising politicians who "want to pass laws at the drop of a hat ... to give in to media pressure".
Speaking to a crowd of the same size at the Republicans party's youth summer school in Le Touquet, one of the towns that has banned the burkini on its beaches, Sarkozy repeated his call for a law to ban the swimsuit and a ban on Islamic head-covering in universities, the civil service and businesses.
Burkini, Islam and migration
"We don't want external signs of religious affiliation in our country," Sarkozy said to applause. "We don't accept it. It's the law, it's our French way of life; it's French tradition; that's how we live and that's how we want to carry on living."
He mocked the "sensitive ears" of people who were "offended" by his proposal to end the right of immigrants' families to join them in France, a suggestion that Juppé has opposed, and called for the UK to set up a centre to examine the asylum requests of the 7-10,000 migrants camped out at Calais.
Sarkozy claimed to be a "realist", sneering at Juppé's call for a "happy identity" and said he would stand up to the "tyranny of minorities".
While Juppé has called for a pact with Muslim leaders, Sarkozy said there could be "no reasonable compromise with radical Islam and political Islam", which he claimed is a threat for France's Jews, priests, homosexuals, women and young people.
Hope and compromise
Juppé was at pains to throw off his rival's portrayal of him as soft and too quick to compromise.
"I don't underestimate the degree of suffering in this country," he said. "France is suffering economically, socially, morally, politically. But I don't want to tell her it's going to be tougher tomorrow ... I want to give hope. That's what I mean by happy identity."
And he pledged to carry out "reforms that sometimes won't taste like honey".
Juppé leads in polls
Nine other candidates are in the running but have little hope of winning the nomination, according to the opinion polls.
One of them, former budget minister Jean-François Copé, said this weekend that both leading have had their chance, while another, former prime minister François Fillon, accused Sarkozy of "half-measures" and Juppé of being obsessed with unity.
Although the latest opinion poll, published by TNS Sofres on Sunday, put Sarkozy and Juppé neck and neck among people who said they would definitely vote in the primary, all others have put Juppé ahead, in another recent one at 38 percent against the former president's 24 percent.
If only supporters who are not party members were to vote, however, Sarkozy would win in a landslide, with 45 percent in the first round and 59 percent in the second, according to TNS Sofres.