Sunni insurgents seized a mainly ethnic Turkmen city in northwestern Iraq on Sunday, while the United States boosted security for its diplomatic staff in Baghdad said some staff had evacuated the embassy.
Brent rose about 0.6 percent to $113.20 per barrel, after touching $114.69 on Friday, its highest since September. Brent added more than $4 last week. U.S. crude rose about 0.5 percent to $107.43, approaching Friday's nine-month high of $107.68.
On Wall Street on Friday, stocks edged higher, but ended with modest losses for the week.
MSCI's broadest index of Asia-Pacific shares outside Japan was slightly lower in early trade, moving away from a three-year high hit a week ago.
Japan's Nikkei stock average dipped 0.4 percent, as the yen crept slightly higher, getting a safe-haven lift from investors' rising risk aversion.
The dollar slipped about 0.1 percent to 101.95 yen, moving back toward a two-week low of 101.60 yen marked on Thursday. The euro edged slightly lower to buy 137.99 yen.
Against the greenback, the euro was steady on the day at $1.3534.
Investors will be focusing on the U.S. Federal Reserve this week, which will conclude a policy meeting on Wednesday. Markets will be watching for any signals on when the U.S. central bank might begin hiking interest rates.
"We expect the Fed to taper asset purchases by a further $10 billion per month and participant projections for growth and unemployment to be revised lower, while inflation is likely to be revised modestly higher," Barclays strategists said.
"As a result, the risk is again tilted toward the Fed's dots conveying a slightly more aggressive path of the hiking cycle," they said, which is likely to provide support for the dollar.
Other data in focus this week is China's latest report on foreign direct investment on Tuesday, and then house price figures on Wednesday. Investors would be concerned if the latter were to show a slowdown in property price growth, raising questions about the outlook for that sector.