Yellen is scheduled to take part in a discussion on global economic issues at London's Royal Academy and a number of other top Fed officials are also due to speak later in the global day.
MSCI's broadest index of Asia-Pacific shares outside Japan added 0.2 percent, while Japan's Nikkei put on 0.5 percent.
The pound shed almost three U.S. cents in hectic trade, or close to 2 percent, while futures for the FTSE lost 0.5 percent on speculation the left-leaning Labour Party might actually be able to form a coalition government.
With U.K. elections, an European Central Bank policy meeting where policymakers may take a less dovish stance, and former FBI director James Comey's Senate testimony on all set for Thursday, market participants will be wary of taking big positions.
The S&P/ASX 200 tumbled 1.02 percent, driven by broad declines in the utilities, financials and energy sub-indexes. Major banking and resource stocks traded in the red.
The attackers first drove into pedestrians on London Bridge, then headed to Borough Market before being shot by police. At least seven were killed and 48 injured following the attack. Twelve individuals have already been arrested in the wake of the attack, which the Metropolitan Police said is being treating as a terrorist incident.
Data shows foreign investors, who make up 70 percent of trading activity in the Tokyo market, rushed to cover short positions as a rally from the year's low on April 17 gathered momentum.
The Nikkei 225 edged 0.13 percent lower in early trade. The S&P/ASX 200 was effectively flat, trading 0.01 percent lower.
Japan's Nikkei 225 was down 1.16 percent on the back of the stronger yen. The ASX 200 was lower by 0.73 percent, driven mainly by in its materials and energy sub-indexes, which sank 2.54 percent and 1.68 percent respectively.
Japan's Nikkei 225 fell 1.19 percent. The Nikkei share average is trading at its lowest since December last year. The ASX 200 dipped 0.05 percent while the Kospi was marginally higher and trading 0.07 percent higher.
Japan's Nikkei added 0.8 percent early on Friday after touching a four-month low on Thursday. It's set to post a 0.85 percent loss for the week.
Lingering fears of a possible trade war kept Asian markets on edge. MSCI's broadest index of Asia-Pacific shares outside Japan dipped 0.2 percent
Asian share markets were down in skittish early trade on Tuesday as investors held their breath ahead of a potentially tense meeting between US President Donald Trump and his Chinese counterpart Xi Jinping later this week.
South Korea's trade data for March released over the weekend added to the evidence of an improving global demand outlook, with the country's exports rising more than expected.
Japan's core consumer prices rose 0.2 percent in February year-on-year, marking the fastest growth in nearly two years. But household spending fell 3.8 percent in February from a year earlier, missing estimates for a 1.7 percent fall. Meanwhile, Japan's February jobless rate declined to 2.8 percent, its lowest rate since June 1994, and marked an improvement in the labor market.
Japan's Nikkei stock index was down 0.2 percent, while Australian shares firmed, helped by gains in oil prices. Strong energy shares had helped the US S&P 500 end higher overnight.
Japan's Nikkei added 0.1 percent, having climbed over 1 percent the previous day.
Japan's Nikkei 225 rose 0.82 percent, recovering most of its losses of 276 points, or 1.44 percent, seen yesterday.
Japanese benchmark Nikkei 225 dropped more than 1.5 percent and the safe-haven yen strengthened.
Asian share markets were in limbo as a vote on the American Health Care Act might not happen until later Friday or Monday, as it meets opposition from warring factions within the Republicans themselves.
Japan's Nikkei gained 0.25 percent, thanks to a weaker yen.
In early trade, MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.1 percent, staying near a 15-month high it touched on Monday, with South Korean shares hitting two-year highs.
Chinese mainland shares were mixed on Monday morning, with the Shanghai composite up 0.13 percent and the Shenzhen composite flat. Hong Kong's Hang Seng added 0.21 percent.
Japan's Nikkei lost 0.4 percent, and is poised for a 0.5 percent loss for the week.