"We must see real progress this week, especially in developing an effective accountability mechanism which will hold governments to account for clear targets every year for the next five years," said Tearfunds advocacy director, Paul Cook.
A three-day summit at the United Nations headquarters opened on Monday with a plea by Secretary-General Ban Ki-moon to "keep the promise" of helping the world's poor by 2015.
"There is no global project more worthwhile," Ban said. "Let us send a strong message of hope. Let us keep the promise."
Ban convened the summit to accelerate progress on the MDGs as the five-year countdown to the target date for their fulfillment begins.
The MDGs, which were devised in 2000, include halving extreme poverty by half, halting the spread of HIV/AIDS, providing universal primary education and reducing by two thirds the under-five mortality rate.
"Real results" have been made over the last decade, Ban acknowledged on Monday, pointing to the increase in school enrollment rates and expanded access to clean water.
"We have more development success stories than ever before," he noted. "The transformative impact of the MDGs is undeniable. This is an achievement we can [be] proud of."
But the clock is ticking, he added, and there is much more to do.
The U.N. Secretary General has acknowledged that many countries, especially in sub-Saharan Africa, are falling short of the targets. But the world as a whole is on track to reducing poverty, he noted.
He urged world leaders to "stay true" to achieving the Goals on time.
Ahead of the summit, Christian leaders from the World Evangelical Alliance, the Salvation Army, the Anglican Communion, Micah Challenge and Sojourners sent a letter to the U.S., the African Union and the European Union calling for a "clear and strong commitment" to the promises made.
"Now is the time to advance bold new plans that ensure we do not fail to meet the Goals, especially those that are most off-track," they stated. "With five years remaining until the deadline for the Goals is reached, now is the time for tenacious leadership."
The Christian leaders have organized a prayer day for October 10 focused on the fulfillment of the MDGs.
Cook of Tearfund, a relief and development charity based in the U.K., has stressed to world leaders that churches must be recognized as "essential partners" in their plans to achieve the Goals.
"We must embrace the opportunities that churches and faith communities bring in working with poor communities at grassroots levels to transform their own lives forever," he said.
On Wednesday, Ban is expected to unveil a global strategy for improving womens and childrens health, one of the target areas in the MDGs.
"No area has more potential to set off a ripple effect a virtuous cycle across the Goals than womens health and empowerment," he said. "All the key players have lined up behind this effort." Christian Post