"We spoke about it today, but we didn't talk about a date or time," Ratas told state broadcaster ERR after Pence began a visit to the tiny frontline state yesterday.
The Patriot is a mobile, ground-based system designed to intercept incoming missiles and warplanes.
"We talked about the upcoming (Russian military) manoeuvres near the Estonian border... And how Estonia, the United States and NATO should monitor them and exchange information," Ratas said.
Concern in Estonia and fellow Baltic states Latvia and Lithuania surged after Russia annexed Crimea from Ukraine in 2014 and stepped up military exercises.
Pence, in remarks to journalists in the Estonian capital of Tallinn, spoke in strong but general terms about US support for eastern European countries.
Today, he heads to Georgia -- a non-NATO member that is also worried about Russia -- and then to Montenegro, which became NATO's 29th member on June 5.
"Our message to the Baltic states - my message when we visit Georgia and Montenegro - will be the same: 'To our allies here in Eastern Europe, we are with you, we stand with you on behalf of freedoms'."
Pence also said the Trump administration had "made it clear" that it stood behind NATO's Article 5 commitment that an attack on one member was an attack on all -- a pledge that Trump has been criticised for failing to spell out emphatically.
He is also to visit troops from the Enhanced Forward Presence programme, under which NATO has deployed four battalions to the Baltic states and Poland to bolster the alliance's eastern flank.
Moscow last year deployed nuclear-capable Iskander missiles into its Kaliningrad exclave, which borders Lithuania and Poland.
It is due to hold massive military exercises in Belarus and Kaliningrad in September. The so-called "Zapad" ("West") drills will see Russia showcase new hardware and upgrade existing systems in its western military region.
Some 800 Georgian and 1,600 US troops are taking part in the Noble Partner 2017 drills -- the largest ever in Georgia since it fought a brief war with Russia in 2008.
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