US President Barack Obama described the incident in the east Ghouta region of Damascus - which rebels say killed as many as 1000 civilians - as a "big event of grave concern".
But he appeared unwilling to entangle America in another costly war, stressing: "The notion that the US can somehow solve what is a sectarian, complex problem inside of Syria sometimes is overstated."
Writing in today's Herald, Mr Alexander condemned the UN response earlier this week as insufficient and called for Britain and its allies on the Security Council to secure a fresh resolution, which "not only condemns the use of chemical weapons but specifies the mandate of the UN inspection team already in Syria to include east Ghouta".
The Labour MP for Paisley and Renfrewshire South insists there is a "real urgency" for the UN inspectors to gain full access to the site, noting how evidence of toxic agents, which make chemical weapons lethal, can "quickly be dispersed and contaminated".
He adds: "To establish beyond doubt the nature but also the perpetrators of this week's strike in East Ghouta, the UN team must be granted access within days."
William Hague, the UK Foreign Secretary, said "Some people would like to say this is some kind of conspiracy brought about by the opposition in Syria. The chances of that are vanishingly small and so we do believe this is a chemical attack by the Assad regime."