Yildirim spoke at the ruling party's first rally ahead of a key April 16 referendum, when the public will vote on whether to approve the changes creating an executive presidency.
"For a strong Turkey, lasting stability, our choice is 'yes'. This is our wish, it will come," Yildirim told the gathering in Ankara of party members and supporters from the country's 81 provinces.
In the boisterous, packed arena, campaign songs floated over the flag-waving crowd with lyrics endorsing a "yes" vote as a tribute to the "July martyrs" killed during last year's failed coup.
Yildirim, upon arrival, handed out red carnations to supporters.
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In his speech he insisted no one would be forced to back the changes, which the government says are necessary for political harmony but which critics fear will create one-man rule under Erdogan.
Under the new constitution, the president will have strengthened executive powers to directly appoint top public officials including ministers.
The post of prime minister would be replaced with one or more vice presidents.
"We are living through a process where all authority is being gathered in one person," he said, quoted by Dogan news agency.
But the government argues the changes would reduce bureaucracy and respect parliament's powers.
"There is no creating fear," Yildirim told the excited crowds. "We want a willing 'yes'."
Some 6,500 police officers were deployed in and around the arena where heavy security was in evidence, state-run news agency Anadolu reported.
In the arena, there were thousands of people, including many young women, most of whom were waving Turkish flags -- noticeably there were no AKP flags -- or carrying banners, including one praising "grand master" Erdogan.
Audience member Ayse Cakmak said she was voting for the presidential system for "more democracy, for a stable country, for our people to live in security".
The heavy focus on encouraging young people to vote "yes" could be seen everywhere in the arena, with one large banner saying: "Turkey's issues are young people's issues.
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