Mr Milburn said the blockade was causing serious problems for NHS staff and patients.
It says the blockade could destabilise the country and lead to a humanitarian catastrophe.
Hamas leaders hope Mr Mursi, who is a fellow Islamist, will end the blockade.
BBC: Egypt's president discusses Gaza blockade with Hamas PM
The blockade was part of action calling on the UK government to scrap plans for Trident renewal.
The blockade is especially frustrating for the impoverished cities that face each other across a closed frontier.
Certainly, the government has found money from somewhere, despite the blockade on its oil sales (see article).
Opposition spokesman Lord Triesman said there was "understandable" concern about the blockade and provision of goods to Gaza.
The President asked the Republican Party to end the blockade on needed and necessary aid for small businesses.
The blockade conditioned not just Israel's attitude to negotiation with the new authorities in Gaza but also Egypt's.
The blockade by Kuki groups was called off on Tuesday morning after the state government agreed to the demand.
The blockade certainly had an effect as testified by Japan's loss of shipping and its dwindling imports of raw materials.
In its strongly worded statement, the Tajik embassy in Moscow accused the Uzbek authorities of deliberately creating the blockade.
The flotilla, he argued, was not aiming to deliver humanitarian aid to Gazans but was trying to break the blockade.
The regional traffic information centre said the blockade caused tailbacks of five kilometres on the Paris-bound carriageway of the A630.
Aid agencies warned the situation is "very precarious" and called on Israel to end the blockade to avert a humanitarian disaster.
They discussed "solutions" relating to the blockade on the coastal territory and "alleviating the suffering" of its residents, Egyptian officials said.
BBC: Egypt's president discusses Gaza blockade with Hamas PM
It says the blockade is needed to stop the transit of weaponry to be used by militants in attacks on Israel.
Britain, France, Russia and China are all seeking an end to the blockade, while the Obama administration has labeled it unsustainable.
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Israel insists that the blockade of Gaza has been eased considerably in recent months, says the BBC's Wyre Davies in Jerusalem.
All this is happening while the blockade in Iran has taken out as much as 1 million barrels of daily supply.
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All of the blockade protesters were removed from the construction sites by 2 p.m. and 12 of them were arrested, he said.
If Israel had ended the blockade, Hamas may have renewed the truce.
As well as the blockade, it blames war damage and chronic underinvestment.
The blockade of Armenia's borders by Azerbaijan and Turkey looks like continuing.
The government negotiated a suspension of the blockade of the Karakoram highway.
But the blockade of Gaza is an essential guarantee of Israel's security.
About 700 activists - including 400 Turks - were trying to break the blockade of the Gaza Strip by bringing in 10, 000 tonnes of aid.
So, with Israeli eyes, the blockade will be lifted when there are efficient controls of the airport, the seaports and the land-crossings on Lebanon's borders.
Nitrates, found in faeces and fertiliser, are linked to the doubling of the incidence of watery diarrhoea in children since the blockade began, it says.
The commission's ambit, in Mr Netanyahu's blueprint, would also focus purely on whether the blockade of Gaza and the seizure of the peace flotilla were legal.
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