"We say thank you to the junta for their intervention," an opposition spokesman, Bazoum Mohamed, told the rally.
"We are for the restoration of democracy and we are committed to joining the army in this mission."
A military leader, Harouna Djibrilla Adamou, told the crowds: "We thank you for your overwhelming support."
"What we did was in the best interest of Niger. We ask you to stay calm, we're here for you, we're listening and we assure you that we will never let you down," he said.
An opposition coalition formed last year to protest against Mr Tandja's constitutional changes has written to the new military leadership, calling for a new constitution and for free and transparent elections to be organised.
However, Niger's new rulers have so far not mentioned a return to civilian rule.
'Safe and well'
Troops stormed the presidential palace during a cabinet meeting on Thursday afternoon, seizing Mr Tandja and his ministers before announcing that they were suspending the constitution and dissolving all state institutions.
Col Goukoye Abdul Karimou read a statement signed by Col Salou Djibo
Niger's new leaders have promised to turn the country into an example of "democracy and good governance" and save its people from "poverty, deception and corruption".
A senior army officer, Col Salou Djibo, was named head of a military government.
Mr Tandja, a 71-year-old former army officer, was first elected in 1999 and was returned to power in an election in 2004.
His second term in office expired in December, but was extended to allow him to complete major investment projects.
A junta spokesman, Col Goukoye Abdul Karimou, told the BBC on Friday that the president was "safe and well".
Niger has experienced long periods of military rule since independence from France in 1960.
It is one of the world's poorest countries, but Mr Tandja's supporters argue that his decade in power has brought a measure of economic stability.
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