Middle East Minister Alistair Burt has said there is "no information" to suggest UK-made weapons had been used against civilians in Gaza.
Responding to a question from Edinburgh East MP Tommy Sheppard, Burt said the government would be "extremely concerned" if any proof emerged that arms sold to Israel had been put into force during Monday's violence.
Around 60 died and thousands were hurt in actions that provoked widespread condemnation.
Sheppard asked Burt if he would "make it his policy to find out whether or not arms supplied in this country were used for the mass slaughter of unarmed protesters in the violence".
Burt responded that checks are carried out before export licences are granted, adding that it is "not possible" to do the same for end uses.
The exchange came during a Commons session that saw Burt call for an independent inquiry into the events in Gaza while under sustained pressure from MPs.
He suggested Monday's events could be "an opportunity for a springboard to peace," going on: "We have no side here, except with the victims."
But LibDem Christine Jardine, MP for Edinburgh West, called the situation "utterly depressing and heartbreaking", asking if the government will now ensure that "as well as protecting Israel’s right to exist, we defend the right of the Palestinian people to have exactly the same rights and international status as Israelis".
However, Ross Thomson, who represents Aberdeen South, directed his criticism at Hamas, saying its officials had been "actively encouraging protestors to be martyrs and bussing rioters to the border for them to sling Molotov cocktails and fireballs across it and to tear down fencing". The Tory MP went on: "Hamas is using civilians as a cover to incite violence."
Earlier in the day a spokesperson for Theresa May called the violence "destructive to peace efforts", adding: "Palestinians have the right to protest but these protests must be peaceful. We are concerned that extremist elements may be seeking to hijack peaceful protests to further their own objectives.
"Israel has the right to defend its borders and we do not question that. However, the use of live fire is deeply troubling and has led to significant loss of life. We urge Israel to show greater restraint."
Mark Regev, Israel's ambassador to the UK, said the gunfire had been "measured" and "surgical".
But Labour's Emily Thornberry told the Commons the shots were fired at "unarmed protestors who posed no threat" in what she called "the culmination of six weeks of an apparently calculated and deliberate policy to kill and maim".
She continued: "Many of them were shot in the back, many of them were shot hundreds of metres from the border and many of them were children."