Meanwhile, the global chemical weapons watchdog has said it will send a fact-finding team to the site in Douma.
It's not yet clear what kind of military action May is reportedly considering taking.
Russian Federation and Syria have called for the OPCW to send its experts to the rebel-held town of Douma, where toxic gas was allegedly used in an attack on Saturday that killed dozens.
The Associated Press reported that U.S. officials and counterparts in Britain and France had been discussing a possible joint military response, with sources saying the allies had been weighing up a strike as early as the end of the week.
The body said pilots should exercise caution in and around Syria over the next 72 hours, due to expected air strikes on Syria.
While Haley and Russian Ambassador Vassily Nebenzia were seen greeting each other with handshakes and kisses on the cheek prior to the meeting, the mood quickly changed as the diplomats hurled accusations at each other. The US has sought a new committee to investigate the suspected attacks.
Haley said Russian Federation was to blame for the council's failure to take action on Syria, now in its 8th year of war.
He announced that Russian Federation would propose a "transparent and honest" investigation at the Security Council.
"We are not surprised by this reckless escalation from a regime like the one in the United States, which has and continues to sponsor terrorism in Syria", said the statement, carried by state media.
"If the government is proposing to expand its military activity in Syria, they should seek a fresh parliamentary mandate for that action", a spokeswoman for Britain's opposition Labour Party said.
U.S. Ambassador Nikki Haley told the Security Council on Monday that both Russian Federation and Iran could stop the Syrian government's "murderous destruction", adding that Moscow's hands are "covered in the blood of Syrian children".
"I don't want to telegraph what I am doing or what I am thinking", Mr. Trump said.
US officials said military options were being developed.
The worldwide chemical weapons watchdog said it will send "shortly" a fact-finding mission to the Syrian town where the suspected gas attack took place, after receiving a request from the Syrian government and its Russian backers to investigate the allegations.
French President Emmanuel Macron has indicated that he supports a "strong, joint response" to the reported chemical attack.
She is expected to comment on the situation again on Wednesday during a visit to Birmingham.
Syria denies using chemical weapons.
U.S. President Donald Trump and Western allies are discussing possible military action to punish Syria's President Bashar Assad for a suspected poison gas attack on Saturday on a rebel-held town that long had held out against government forces.