The country has been ruled by a junta following the ousting of President Mohamed Bazoum nearly two weeks ago.
There have been suggestions the coup leaders have asked for help from Wagner, which is known to be present in neighbouring Mali.
Mr Blinken said he did not think Russia or Wagner instigated Niger’s coup.
However the US was worried about the group “possibly manifesting itself” in parts of the Sahel region, he told the BBC’s Focus on Africa programme
“I think what happened, and what continues to happen in Niger was not instigated by Russia or by Wagner, but… they tried to take advantage of it.
“Every single place that this Wagner group has gone, death, destruction and exploitation have followed,” said Mr Blinken.
“Insecurity has gone up, not down”.
He added that there was a “repeat of what’s happened in other countries, where they brought nothing but bad things in their wake”.
Both the US and France operate military bases in Niger as part of operations to disrupt jihadist groups operating in the wider region. Niger became the main base for French troops after they were told to leave Mali following a coup there.
Wagner is believed to have thousands of fighters in countries including the Central African Republic (CAR) and Mali, where it has lucrative business interests but also bolsters Russia’s diplomatic and economic relations.
The group’s fighters have been accused of widespread human rights abuses in several African countries.
Despite this, there has been speculation Niger’s army has asked Wagner for assistance as the country faces the possibility of military intervention.
On Monday, US Deputy Secretary of State Victoria Nuland held what she described as “difficult and frank” talks with the coup leaders, whom she said understood the risks of working with the mercenaries.
Mr Bazoum, who is currently being detained, has also spoken of his concerns about Wagner’s influence in Africa.
“With an open invitation from the coup plotters and their regional allies, the entire central Sahel region could fall to Russian influence via the Wagner Group, whose brutal terrorism has been on full display in Ukraine,” he wrote in an opinion piece for the Washington Post published last week.
It is currently unclear if Wagner fighters have entered the country but the prominent Wagner-affiliated Telegram channel Grey Zone said on Monday that some 1,500 of its fighters had recently been sent to Africa.
It did not specify where on the continent they had allegedly been deployed.
Wagner’s leader, Yevgeny Prigozhin has urged the junta to “give us a call” in a voice message uploaded to Telegram on Tuesday.
“We are always on the side of the good, on the side of justice, and on the side of those who fight for their sovereignty and for the rights of their people,” he said.
Niger is a former French colony and the coup has led to a wave of anti-France and pro-Russian sentiment in the country – similar to that experienced by neighbours Mali and Burkina Faso, which have both pivoted towards Moscow since their own coups.
The two countries, which are both suspended from West African regional bloc Ecowas, sent a delegation to Niamey to reassure the coup leaders they will come to their defence against the other West African nations and their Western allies if needed.
“I would like to remind you that Burkina Faso, Mali and Niger have been dealing for over 10 years with the negative… consequences of Nato’s hazardous adventure in Libya,” Mali government spokesperson Abdoulaye Maiga said during the visit.
“One thing is certain, [Mali’s] President Goita and [Burkina Faso’s] President Traoré have clearly said no, no and no. We will not accept military intervention in Niger. They are coming for our survival.”
Meanwhile Niger’s junta has refused to receive a delegation of representatives from West African regional bloc Ecowas, the African Union and UN, which was due to arrive in the capital Niamey on Tuesday.
In a letter seen by AFP on Tuesday, the coup leaders said the group’s security could not be guaranteed because of “public anger and revolt” over sanctions imposed by Ecowas.
Ecowas had given Niger’s coup leaders until Sunday to stand down and restore Mr Bazoum to the presidency and are now due to meet on Thursday to decide what to do next.
Niger’s junta has appointed the country’s former finance minister, Ali Mahaman Lamine Zeine, as the country’s new prime minister following the coup.
Mr Zeine replaces Mahamadou Ouhoumoudou, who was in Europe during the coup.
