Nurturing care is crucial for children's ongoing development during the pre-primary education period, or the next 1000 days of life. We generated nationally representative prevalence estimates of access to ten basic indicators of nurturing care among children aged 3-4 years in low-income and middle-income countries (LMICs). We applied multiple imputation and predictive modelling to data on children living in LMICs. Individual-level data on ten indicators were from UNICEF's Multiple Indicator Cluster Surveys and the Demographic Health Surveys Program, and we included data on all children aged 36 to 59 months for whom the surveys asked relevant questions on parenting and child development. We defined minimally adequate care as receiving at least one of two indicators in each of five dimensions of nurturing care: responsive caregiving, early learning, safety and security, nutrition, and health. We used a two-step multi-level multiple imputation procedure to address missing data across individuals, indicators, and countries. Using imputed datasets, we generated a set of expected-a-posteriori estimates of the percentage and overall number of children receiving each indicator of nurturing care, as well as overall minimally adequate care, for each country, country income grouping, and region, and across all LMICs. For the 54 countries with individual-level data on all indicators, we also produced subgroup estimates of nurturing care on the basis of household wealth, child sex, and urbanicity. We included individual-level data collected between 2005 and 2019 on 426 349 children aged 3-4 years in 104 LMICs. Across the 137 LMICs considered in our modelling, we estimated that 62·0 million (90% credible interval [CrI] 51·6-71·7) children aged 3-4 years, equivalent to 25·4% (90% CrI 21·2-29·4) of that age group in LMICs, were receiving minimally adequate nurturing care at the time of assessment, leaving 181·9 million (172·2-192·3) without adequate care. Access to care was highest for nutrition (86·2% [84·2-88·2], or 210·3 million [205·4-215·1], with healthy weight), and lowest for early learning (29·3% [21·5-39·6], or 71·5 million [52·5-96·6], in early childhood care and education), responsive caregiving (29·7% [25·6-34·9], or 72·4 million [62·4-85·0], experiencing adequate stimulation from non-maternal caregivers), and safety and security (32·3% [28·3-36·7], or 78·7 million [68·9-89·5], living without physical punishment). Gaps were evident in the estimates, with 50·8% (38·3-60·7) of children from upper middle-income countries receiving minimally adequate care compared with 5·6% (4·8-6·4) in low-income countries. Within 54 countries with complete child-level data, 10·7% (10·4-10·9) of children from households in the lowest wealth quintile had access to minimally adequate care compared with 41·2% (40·7-41·7) in the highest quintile. Inequalities were also large by urbanicity (17·7% [17·5-18.0] rural vs 32·2% [31·8-32.6] urban) but smaller by child sex (23·9% [23·6-24·2] girls vs 22·1% [21·9-22·4] boys). Most children in LMICs are not receiving minimally adequate nurturing care during the next 1000-day period. Further investments in indicator measurement and resources for preschool-age children are needed, particularly for low-income populations and in the domains of responsive caregiving, early learning, and safety and security. None.