Located about 65 kilometers (40 miles) away from Manila, Taal is one of the country's most active volcanoes, although it has not had a major eruption since 1977.
Manila global airport has suspended flights over the eruption of the Taal volcano, located some 55 km to the south.
The local disaster office said it had evacuated more than 2,000 residents living on the volcanic island, which lies inside a bigger lake formed by previous volcanic activity.
The institute recommended a "total evacuation" of the Taal Volcano Island as well as additional evacuations in areas within an 8-mile radius of the volcano's main crater.
The Manila International Airport Authority suspended arrivals and departures.
Ash from the volcano has fallen as far as the capital, and the plume was visible from the nearby tourist hotspot of Tagaytay.
President Rodrigo Duterte had instructed authorities to move people within the perimeter of Taal out of the danger zone, his spokesman said in a statement.
In a bulletin on Sunday at 2.30 pm, Phivolcs said it raised the status of the volcano from warning level 1, which means abnormal, to warning level 2, which means more unrest.
Jon Patrick Yen, a restaurant customer in Tagaytay, told Reuters: "We were having lunch when we heard rumbling".
In December, 19 people died after a New Zealand volcano island unexpectedly erupted in a forceful explosion of scorching steam, gas and ash.
"I did not expect to see such (a) spectacle".
The heavy ash fall also reached the province of Cavite, prompting the provincial government to suspend classes on Monday and urge residents to stay indoors.
The Philippines is situated in the seismic area known as the Ring of Fire which encircles the Pacific Ocean. "We just went by to eat".